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  • PIR Codes with Short Block Length
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-17
    Sascha Kurz, Eitan Yaakobi

    In this work private information retrieval (PIR) codes are studied. In a k-PIR code, s information bits are encoded in such a way that every information bit has k mutually disjoint recovery sets. The main problem under this paradigm is to minimize the number of encoded bits given the values of s and k, where this value is denoted by P(s, k). The main focus of this work is to analyze P(s, k) for a large

    更新日期:2021-01-18
  • An extending theorem for s -resolvable t -designs
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-17
    Tran van Trung

    An extending theorem for s-resolvable t-designs is presented, which may be viewed as an extension of Qiu-rong Wu’s result. The theorem yields recursive constructions for s-resolvable t-designs, and mutually disjoint t-designs. For example, it can be shown that if there exists a large set LS[29](4, 5, 33), then there exists a family of 3-resolvable 4-\((5+29m, 6, \frac{5}{2}m(1+29m) )\) designs for

    更新日期:2021-01-18
  • Abelian difference sets with the symmetric difference property
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-16
    James A. Davis, J. J. Hoo, Connor Kissane, Ziming Liu, Calvin Reedy, Kartikey Sharma, Ken Smith, Yiwei Sun

    A \((v,k,\lambda )\) symmetric design is said to have the symmetric difference property (SDP) if the symmetric difference of any three blocks is either a block or the complement of a block. The designs associated to the symplectic difference sets introduced by Kantor (J Algebra 33:43–58, 1975) have the SDP. Parker (J Comb Theory Ser A 67:23–43, 1994) claimed that the symplectic design on 64 points

    更新日期:2021-01-18
  • Maximal sets of mutually orthogonal frequency squares
    Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-16
    Nicholas J. Cavenagh, Adam Mammoliti, Ian M. Wanless

    A frequency square is a square matrix in which each row and column is a permutation of the same multiset of symbols. A frequency square is of type \((n;\lambda )\) if it contains \(n/\lambda \) symbols, each of which occurs \(\lambda \) times per row and \(\lambda \) times per column. In the case when \(\lambda =n/2\) we refer to the frequency square as binary. A set of k-MOFS\((n;\lambda )\) is a

    更新日期:2021-01-18
  • Approximability of open k -monopoly problems
    Theory Comput. Syst. (IF 0.497) Pub Date : 2021-01-14
    Sounaka Mishra, B. Arjuna Krishna, Shijin Rajakrishnan

    We consider approximability of two optimization problems called Minimum Open k-Monopoly (Min-Open-k-Monopoly) and Minimum Partial Open k-Monopoly (Min-P-Open-k-Monopoly), where k is a fixed positive integer. The objective, in Min-Open-k-Monopoly, is to find a minimum cardinality vertex set \(S \subseteq V\) in a given graph G = (V,E) such that \(|N(v) \cap S| \geq \frac {1}{2} |N(v)| + k\), for every

    更新日期:2021-01-18
  • Hybrid (b, c)-inverses and five finiteness properties in rings, semigroups, and categories
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-17
    Michael P. Drazin

    Abstract Given elements a, b, c of any associative ring R with 1, then a is called right hybrid (b, c)-invertible if there exists y ∈ R such that yay = y , y R = b R and rann ( y ) = rann ( c ) . It is shown that such y exists if and only if c ∈ cabR and rann ( cab ) ⊆ rann ( b ) , in which case y is unique. With an appropriate generalization of the right annhilator rann (.), this result is extended

    更新日期:2021-01-18
  • Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-17
    Haruhisa Enomoto

    Abstract For an element w of a simply-laced Weyl group, Buan-Iyama-Reiten-Scott defined a subcategory F ( w ) of the module category over the preprojective algebra of Dynkin type. This paper studies categorical properties of F ( w ) using the root system. We show that simple objects in F ( w ) bijectively correspond to Bruhat inversion roots of w, and obtain a combinatorial criterion for F ( w ) to

    更新日期:2021-01-18
  • Unified products of Leibniz conformal algebras
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-16
    Yanyong Hong; Lamei Yuan

    Abstract The aim of this article is to provide an answer to the C [ ∂ ] -split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on E = R ⊕ Q up to an isomorphism such that R is a Leibniz conformal subalgebra. For this purpose, a unified product of Leibniz conformal algebras is introduced. Using this tool, two cohomological

    更新日期:2021-01-18
  • Lie generalized derivations on bound quiver algebras
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-16
    Abderrahim Adrabi; Driss Bennis; Brahim Fahid

    Abstract In this paper, we investigate Lie generalized derivations on bound quiver algebras associated with a finite acyclic quiver. The first main result shows that every bound quiver algebra associated with a finite acyclic quiver has the properness Lie generalized derivation property. The second main result investigates the uniqueness property. Namely, among other things, we show that a bound quiver

    更新日期:2021-01-18
  • A new class of distance-optimal binary cyclic codes and their duals
    Appl. Algebra Eng. Commun. Comput. (IF 0.6) Pub Date : 2021-01-17
    Kaiqiang Liu, Wenli Ren, Feng Wang, Jianpeng Wang

    Let \(m=8k\) and \(\alpha\) be a primitive element of the finite field \({{\mathbb {G}}{\mathbb {F}}}(2^m)\), where \(k\ge 2\) is an integer. In this paper, a class of binary cyclic codes \({{\mathcal {C}}}_{(u,v)}\) of length \(2^m-1\) with two nonzeros \(\alpha ^{-u}\) and \(\alpha ^{-v}\) is studied, where \((u,v)=(1,(2^{m}-1)/17)\). It turns out that \({{\mathcal {C}}}_{(u,v)}\) has parameters

    更新日期:2021-01-18
  • Universal Equivalence of Generalized Baumslag–Solitar Groups
    Algebra Logic (IF 0.624) Pub Date : 2020-11-29
    F. A. Dudkin

    A finitely generated group acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group (a GBS group). Every GBS group is the fundamental group π1(𝔸) of a suitable labeled graph 𝔸. We prove that if 𝔸 and 𝔹 are labeled trees, then the groups π1(𝔸) and π1(𝔹) are universally equivalent iff π1(𝔸) and π1(𝔹) are embeddable into

    更新日期:2021-01-18
  • Obstructions to deforming curves on an Enriques-Fano 3-fold
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-11
    Hirokazu Nasu

    We study the deformations of a curve C on an Enriques-Fano 3-fold X⊂Pn, assuming that C is contained in a smooth hyperplane section S⊂X, that is a smooth Enriques surface in X. We give a sufficient condition for C to be (un)obstructed in X, in terms of half pencils and (−2)-curves on S. Let HilbscX denote the Hilbert scheme of smooth connected curves in X. By using the Hilbert-flag scheme of X, we

    更新日期:2021-01-16
  • Multivariate Alexander quandles, II. The involutory medial quandle of a link (corrected)
    J. Knot Theory Ramif. (IF 0.426) Pub Date : 2020-12-30
    Lorenzo Traldi

    Joyce showed that for a classical knot K, the involutory medial quandle IMQ(K) is isomorphic to the core quandle of the homology group H1(X2), where X2 is the cyclic double cover of 𝕊3, branched over K. It follows that |IMQ(K)|=|detK|. In this paper, the extension of Joyce’s result to classical links is discussed. Among other things, we show that for a classical link L of μ≥2 components, the order

    更新日期:2021-01-16
  • Generalized Grigorchuk’s overgroups as points in the space of marked 8-generated groups
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-12-29
    Supun T. Samarakoon

    First Grigorchuk group 𝒢 and Grigorchuk’s overgroup 𝒢̃, introduced in 1980, are self-similar branch groups with intermediate growth. In 1984, 𝒢 was used to construct the family of generalized Grigorchuk groups {Gω|ω∈{0,1,2}ℕ}, which has many remarkable properties. Following this construction, we generalize the Grigorchuk’s overgroup 𝒢̃ to the family {G̃ω|ω∈{0,1,2}ℕ} of generalized Grigorchuk’s

    更新日期:2021-01-16
  • The existence of primitive normal elements of quadratic forms over finite fields
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-12-29
    Himangshu Hazarika; Dhiren Kumar Basnet; Stephen D. Cohen

    For q=3r (r∈ℕ), denote by 𝔽q the finite field of order q and for a positive integer m≥2, let 𝔽qm be its extension field of degree m. We establish a sufficient condition for existence of a primitive normal element α such that f(α) is a primitive element, where f(x)=ax2+bx+c, with a,b,c∈𝔽qm satisfying b2≠ac in 𝔽qm.

    更新日期:2021-01-16
  • Skew cyclic codes over 𝔽4R
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-12-28
    Nasreddine Benbelkacem; Martianus Frederic Ezerman; Taher Abualrub; Nuh Aydin; Aicha Batoul

    This paper considers a new alphabet set, which is a ring that we call 𝔽4R, to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize 𝔽4R-skew cyclic codes. Interesting connections between the image

    更新日期:2021-01-16
  • Duplication methods for embeddings of real division algebras
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-12-23
    Marina Tvalavadze; Noureddine Motya; Abdellatif Rochdi

    We introduce two groups of duplication processes that extend the well known Cayley–Dickson process. The first one allows to embed every 4-dimensional (4D) real unital algebra 𝒜 into an 8D real unital algebra denoted by FD(𝒜). We also find the conditions on 𝒜 under which FD(𝒜) is a division algebra. This covers the most classes of known 4D real division algebras. The second process allows us to

    更新日期:2021-01-16
  • Representation theory of symmetric groups and the strong Lefschetz property
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-12-17
    Seok-Jin Kang; Young Rock Kim; Yong-Su Shin

    We investigate the structure and properties of an Artinian monomial complete intersection quotient A(n,d)=𝕂[x1,…,xn]/(x1d,…,xnd). We construct explicit homogeneous bases of A(n,d) that are compatible with the Sn-module structure for n=3, all exponents d≥3 and all homogeneous degrees j≥0. Moreover, we derive the multiplicity formulas, both in recursive form and in closed form, for each irreducible

    更新日期:2021-01-16
  • Buchsbaumness of the associated graded rings of filtration
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-30
    Kumari Saloni

    Let (A,𝔪) be a Noetherian local ring of dimension d>0 and I an 𝔪-primary ideal of A. In this paper, we discuss a sufficient condition, for the Buchsbaumness of the local ring A to be passed onto the associated graded ring of filtration. Let ℐ denote an I-good filtration. We prove that if A is Buchsbaum and the 𝕀 -invariant, 𝕀(A) and 𝕀(G(ℐ)), coincide then the associated graded ring G(ℐ) is Buchsbaum

    更新日期:2021-01-16
  • Zero-divisor graph of semisimple group-rings
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-25
    Krishnan Paramasivam; K. Muhammed Sabeel

    Let Γ(R), ΓE(R), ΓAnn(R) denote the zero-divisor graph, compressed zero-divisor graph and annihilating ideal graph of a commutative ring R, respectively. In this paper, we prove that ΓE(R)≅ΓAnn(R) for a semisimple commutative ring R and represent Γ(R) as a generalized join of a finite set of graphs. Further, we study the zero-divisor graph of a semisimple group-ring 𝔽qCn and proved several structural

    更新日期:2021-01-16
  • Kac–Wakimoto conjecture for the periplectic Lie superalgebra
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-24
    Inna Entova-Aizenbud; Vera Serganova

    We prove an analogue of the Kac–Wakimoto conjecture for the periplectic Lie superalgebra 𝔭(n), stating that any simple module lying in a block of non-maximal atypicality has superdimension zero.

    更新日期:2021-01-16
  • Good codes from metacyclic groups II
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-20
    Samir Assuena

    In this paper, we consider semisimple group algebras 𝔽qG of split metacyclic groups over finite fields. We construct left codes in 𝔽qG in the case when the order G is pmℓn, where p and ℓ are different primes such that gcd(q,p,ℓ)=1 extend the construction described in a previous paper, determine their dual codes and find some good codes.

    更新日期:2021-01-16
  • Monogenic reciprocal trinomials and their Galois groups
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-11
    Lenny Jones

    Let Cn denote the cyclic group of order n, and let Hol(Cn) denote the holomorph of Cn. In this paper, for any odd integer m≥3, we find necessary and sufficient conditions on an integer A, with |A|≥3, such that 𝔉m,A(x)=x2m+Axm+1 is irreducible over ℚ. When m=q≥3 is prime and 𝔉q,A(x) is irreducible, we show that the Galois group over ℚ of 𝔉q,A(x) is isomorphic to either Hol(Cq) or Hol(C2q), depending

    更新日期:2021-01-16
  • Prime avoidance property
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-11
    A. Azarang

    Let R be a commutative ring, we say that 𝒜⊆Spec(R) has prime avoidance property, if I⊆⋃P∈𝒜P for an ideal I of R, then there exists P∈𝒜 such that I⊆P. We exactly determine when 𝒜⊆Spec(R) has prime avoidance property. In particular, if 𝒜 has prime avoidance property, then 𝒜 is compact. For certain classical rings we show the converse holds (such as Bezout rings, QR-domains, zero-dimensional rings

    更新日期:2021-01-16
  • Artinian local cohomology modules of cofinie modules
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-07
    Kamal Bahmanpour

    Let (R,𝔪) be a commutative Noetherian complete local ring and I be a proper ideal of R. Suppose that M is a nonzero I-cofinite R-module of Krull dimension n. In this paper, it shown that dimR/(I+AnnRH𝔪n(M))=n. As an application of this result, it is shown that dimR/(I+𝔭)=n, for each 𝔭∈AttRH𝔪n(M). Also it shown that for each j≥0 the submodule Σj(M):=∪{K:K≤M and dimK≤j} of M is I-cofinite, dimR

    更新日期:2021-01-16
  • Locally finite complexes, modules and generalized information systems
    J. Algebra Appl. (IF 0.61) Pub Date : 2020-11-07
    G. Chiaselotti; F. Infusino

    Simplicial complexes (here briefly complexes) are set systems on an arbitrary set which are object of study in many areas of both mathematics and theoretical computer science. Usually, they are investigated over finite sets. However, in general, when we consider an arbitrary set Ω (not necessarily finite) and a complex 𝒞 on Ω, the most natural property related to finiteness is the following: for any

    更新日期:2021-01-16
  • Representations of ω-Lie algebras and tailed derivations of Lie algebras
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-12-17
    Runxuan Zhang

    We study the representation theory of finite-dimensional ω-Lie algebras over the complex field. We derive an ω-Lie version of the classical Lie’s theorem, i.e., any finite-dimensional irreducible module of a soluble ω-Lie algebra is 1-dimensional (1D). We also prove that indecomposable modules of some 3D ω-Lie algebras could be parametrized by the complex field and nilpotent matrices. We introduce

    更新日期:2021-01-16
  • Almost inner derivations of Lie algebras II
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-12-12
    Dietrich Burde; Karel Dekimpe; Bert Verbeke

    We continue the algebraic study of almost inner derivations of Lie algebras over a field of characteristic zero and determine these derivations for free nilpotent Lie algebras, for almost abelian Lie algebras, for Lie algebras whose solvable radical is abelian and for several classes of filiform nilpotent Lie algebras. We find a family of n-dimensional characteristically nilpotent filiform Lie algebras

    更新日期:2021-01-16
  • Additive actions on complete toric surfaces
    Int. J. Algebra Comput. (IF 0.512) Pub Date : 2020-11-12
    Sergey Dzhunusov

    By an additive action on an algebraic variety X we mean a regular effective action 𝔾an×X→X with an open orbit of the commutative unipotent group 𝔾an. In this paper, we give a classification of additive actions on complete toric surfaces.

    更新日期:2021-01-16
  • RSS equivalences over a class of Morita rings
    J. Algebra (IF 0.745) Pub Date : 2021-01-15
    Nan Gao; Jing Ma; Xuan-Yu Liu

    For two bimodules NBA and MAB with M⊗AN=0=N⊗BM, the monomorphism category M(A,M,N,B) and its dual, the epimorphism E(A,M,N,B), are introduced and studied. By definition, M(A,M,N,B) is the subcategory of Δ-mod consisting of (X,Y,f,g) such that f:M⊗AX→Y is a monic B-map and g:N⊗BY→X is a monic A-map, where Δ=(ANMB) is a Morita ring. This monomorphism category is a resolving subcategory of Δ-mod if and

    更新日期:2021-01-16
  • Morita equivalence classes of blocks with elementary abelian defect groups of order 32
    J. Algebra (IF 0.745) Pub Date : 2021-01-15
    Cesare Giulio Ardito

    We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.

    更新日期:2021-01-16
  • An intriguing hyperelliptic Shimura curve quotient of genus 16
    Algebra Number Theory (IF 0.92) Pub Date : 2020-11-19
    Lassina Dembélé

    Let F be the maximal totally real subfield of ℚ(ζ32), the cyclotomic field of 32-nd roots of unity. Let D be the quaternion algebra over F ramified exactly at the unique prime above 2 and 7 of the real places of F. Let 𝒪 be a maximal order in D, and X0D(1) the Shimura curve attached to 𝒪. Let C = X0D(1)∕⟨wD⟩, where wD is the unique Atkin–Lehner involution on X0D(1). We show that the curve C has several

    更新日期:2021-01-15
  • Relative crystalline representations and p-divisible groups in the small ramification case
    Algebra Number Theory (IF 0.92) Pub Date : 2020-11-19
    Tong Liu; Yong Suk Moon

    Let k be a perfect field of characteristic p > 2, and let K be a finite totally ramified extension over W(k)[1 p] of ramification degree e. Let R0 be a relative base ring over W(k)⟨t1±1,…,tm±1⟩ satisfying some mild conditions, and let R = R0 ⊗W(k)𝒪K. We show that if e < p − 1, then every crystalline representation of π1e ́ t(SpecR[1 p]) with Hodge–Tate weights in [0,1] arises from a p-divisible group

    更新日期:2021-01-15
  • Graded powerful ideals in a graded integral domain
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-15
    Chahrazade Bakkari; Najib Mahdou; Abdelkbir Riffi

    Abstract In this paper, we introduce and study a generalization of powerful ideals, in the sense of Badawi and Houston, to the context of integral domains graded by a torsionless monoid.

    更新日期:2021-01-15
  • A characterization of algebras generated by idempotents
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-11
    Wei Hu; Zhankui Xiao

    We study algebras generated by idempotents. For finite dimensional algebras over a field, it turns out that these algebras can be characterized by their irreducible modules homologically. Particularly, we obtain that a finite dimensional algebra over an algebraically closed field is generated by idempotents if and only if ExtA1(S,S)=0 for all 1-dimensional A-modules S.

    更新日期:2021-01-14
  • Some remarks on Prüfer rings with zero-divisors
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-11
    Federico Campanini; Carmelo Antonio Finocchiaro

    Let A be the fiber product R×TB, where B→T is a surjective ring homomorphism with regular kernel and R⊆T is a ring extension where T is an overring of R. In this paper we provide a characterization of when A has distinguished Prüfer-like properties and new constructions of Prüfer rings with zero-divisors. Furthermore we give examples of homomorphic images of Prüfer rings that are Prüfer without assuming

    更新日期:2021-01-14
  • On the sum of character degrees coprime to p and p-nilpotency of finite groups
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-11
    Hongfei Pan; Nguyen Ngoc Hung; Yong Yang

    The well-known Thompson theorem on character degrees states that if a prime p divides the degree of every nonlinear irreducible character of a finite group G, then G is p-nilpotent. In this paper, we give a strengthened version of Thompson's theorem in terms of ∑χ∈Irrp′(G)χ(1) and ∑χ∈Irrp′(G)χ(1)2, where Irrp′(G) denotes the set of all ordinary irreducible characters of G of degree coprime to p.

    更新日期:2021-01-14
  • Integrable modules for graded Lie tori with finite-dimensional weight spaces
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-08
    Souvik Pal

    An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite-dimensional weight spaces. Recently the irreducible integrable modules having finite-dimensional weight spaces with non-trivial central action have been classified for a more general class of Lie algebras, namely the graded Lie tori. In this paper

    更新日期:2021-01-14
  • Unitary superalgebras with graded involution or superinvolution of polynomial growth
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-07
    W.D.S. Costa; A. Ioppolo; R.B. dos Santos; A.C. Vieira

    In this paper we study associative unitary superalgebras with graded involution or superinvolution having polynomial growth of the codimension sequence. The first goal is to prove that, for this kind of algebras, the codimension sequence is a polynomial with rational coefficients. Then we shall construct several superalgebras with graded involution or superinvolution realizing the smallest and the

    更新日期:2021-01-14
  • An optimal gap of minimal log discrepancies of threefold non-canonical singularities
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-07
    Jihao Liu; Liudan Xiao

    We show that the minimal log discrepancy of any Q-Gorenstein non-canonical threefold is ≤1213, which is an optimal bound.

    更新日期:2021-01-14
  • Computation of residual polynomial operators of inductive valuations
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-07
    Nathália Moraes de Oliveira; Enric Nart

    Let (K,v) be a valued field, and μ an inductive valuation on K[x] extending v. Let Gμ be the graded algebra of μ over K[x], and κ the maximal subfield of the subring of Gμ formed by the homogeneous elements of degree zero. In this paper, we find an algorithm to compute the field κ and the residual polynomial operator Rμ:K[x]→κ[y], where y is another indeterminate, without any need to perform computations

    更新日期:2021-01-14
  • F-invariants of Stanley-Reisner rings
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-08
    Wágner Badilla-Céspedes

    In prime characteristic there are important invariants that allow us to measure singularities. For certain cases, it is known that they are rational numbers. In this article, we show this property for Stanley-Reisner rings in several cases.

    更新日期:2021-01-14
  • Extension groups between atoms in abelian categories
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-08
    Ryo Kanda

    We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelopes are characterized in terms of those extension groups. We also introduce the virtual duals of the extension groups between atoms to measure the global dimension of the category. A new topological property of atom spectra

    更新日期:2021-01-14
  • Componentwise linearity of projective varieties with almost maximal degree
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-07
    Đoàn Trung CƯỜng; Sijong Kwak

    The degree of a projective subscheme has an upper bound deg(X)≤(e+re) in terms of the codimension e and the reduction number r. It was proved in [3] that deg(X)=(e+re) if and only if X is arithmetically Cohen-Macaulay and has an (r+1)-linear resolution. Moreover, if the degree of a projective variety X satisfies deg(X)=(e+re)−1, then the Betti table is described with some constraints. In this paper

    更新日期:2021-01-14
  • The multiplicative group action on singular varieties and Chow varieties
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-14
    Wenchuan Hu

    We answer two questions of Carrell on a singular complex projective variety admitting the multiplicative group action, one positively and the other negatively. The results are applied to Chow varieties and we obtain Chow groups of 0-cycles and Lawson homology groups of 1-cycles for Chow varieties. A brief survey on the structure of Chow varieties is included for comparison and completeness. Moreover

    更新日期:2021-01-14
  • Robust modelling of implicit interfaces by the scaled boundary finite element method
    Eng. Anal. Bound. Elem. (IF 2.884) Pub Date : 2021-01-13
    Shaima M. Dsouza; A.L.N. Pramod; Ean Tat Ooi; Chongmin Song; Sundararajan Natarajan

    In this paper, we propose a robust framework based on the scaled boundary finite element method to model implicit interfaces in two-dimensional differential equations in nonhomegeneous media. The salient features of the proposed work are: (a) interfaces can be implicitly defined and need not conform to the background mesh; (b) Dirichlet boundary conditions can be imposed directly along the interface;

    更新日期:2021-01-14
  • The space of invariant bilinear forms of the polarization algebra of a polynomial endomorphism: An approach to the problem of Albert
    J. Algebra (IF 0.745) Pub Date : 2020-12-30
    Manuel Arenas

    In this article we explore an approach to the problem of Albert described by U. Umirbaev. We characterize the space of invariant bilinear forms of the polarization algebra of a polynomial endomorphism F:Kn→Kn, where K is a field with characteristic different from two. We obtain some conjectures expressed in the language of polynomial endomorphisms, which are equivalent to the existence of invariant

    更新日期:2021-01-14
  • Finiteness conditions and relative derived categories
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Lingling Tan; Dingguo Wang; Tiwei Zhao

    In this paper, we introduce a class of exact structures in terms of finiteness conditions of modules, which are called n-pure exact structures. We investigate the properties of n-pure derived categories of module categories using n-pure exact structures, and show that n-pure derived categories share many nice properties of classical derived categories. In particular, we show that bounded n-pure derived

    更新日期:2021-01-14
  • Relations between quandle extensions and group extensions
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Yongju Bae; J. Scott Carter; Byeorhi Kim

    In [6] and [7], Joyce and Matveev showed that for given a group G and an automorphism ϕ, there is a quandle structure on the underlying set of G. When the automorphism is an inner-automorphism by ζ, we denote this quandle structure as (G,◃ζ). In this paper, we show a relationship between group extensions of a group G and quandle extensions of the quandle (G,◃ζ). In fact, there exists a group homomorphism

    更新日期:2021-01-14
  • A δ-first Whitehead Lemma
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Arezoo Zohrabi; Pasha Zusmanovich

    We prove that δ-derivations of a simple finite-dimensional Lie algebra over a field of characteristic zero, with values in a finite-dimensional module, are either inner derivations, or, in the case of adjoint module, multiplications by a scalar, or some exceptional cases related to sl(2). This can be viewed as an extension of the classical first Whitehead Lemma.

    更新日期:2021-01-14
  • Z2k-code vertex operator algebras
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Hiromichi Yamada; Hiroshi Yamauchi

    We study a simple, self-dual, rational, and C2-cofinite vertex operator algebra of CFT-type whose simple current modules are graded by Z2k. Based on those simple current modules, a vertex operator algebra associated with a Z2k-code is constructed. The classification of irreducible modules for such a vertex operator algebra is established. Furthermore, all the irreducible modules are realized in a module

    更新日期:2021-01-14
  • Automorphisms of Danielewski varieties
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Sergey A. Gaifullin

    In 2007, Dubouloz introduced Danielewski varieties. Such varieties generalize Danielewski surfaces and provide counterexamples to generalized Zariski cancellation problem in arbitrary dimension. In the present work we describe the automorphism group of a Danielewski variety. This result is a generalization of a description of automorphisms of Danielewski surfaces due to Makar-Limanov.

    更新日期:2021-01-14
  • Degree of Rational Maps versus Syzygies
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    M. Chardin; S.H. Hassanzadeh; A. Simis

    One proves a far-reaching upper bound for the degree of a generically finite rational map between projective varieties over a base field of arbitrary characteristic. The bound is expressed as a product of certain degrees that appear naturally by considering the Rees algebra (blowup) of the base ideal defining the map. Several special cases are obtained as consequences, some of which cover and extend

    更新日期:2021-01-14
  • q-étale covers of cyclic p-gonal covers
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Ángel Carocca; Rubén A. Hidalgo; Rubí E. Rodríguez

    In this paper we study the Galois group of the Galois cover of the composition of a q-cyclic étale cover and a cyclic p-gonal cover for any odd prime p. Furthermore, we give properties of isogenous decompositions of certain Prym and Jacobian varieties associated to intermediate subcovers given by subgroups.

    更新日期:2021-01-14
  • Developable cubics in P4 and the Lefschetz locus in GOR(1,5,5,1)
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Thiago Fassarella; Viviana Ferrer; Rodrigo Gondim

    We provide a classification of developable cubic hypersurfaces in P4. Using the correspondence between forms of degree 3 on P4 and Artinian Gorenstein K-algebras, given by Macaulay-Matlis duality, we describe the locus in GOR(1,5,5,1) corresponding to those algebras which satisfy the Strong Lefschetz property.

    更新日期:2021-01-14
  • Rigged configurations and the ⁎-involution for generalized Kac–Moody algebras
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    B. Salisbury; T. Scrimshaw

    We construct a uniform model for highest weight crystals and B(∞) for generalized Kac–Moody algebras using rigged configurations. We also show an explicit description of the ⁎-involution on rigged configurations for B(∞): that the ⁎-involution interchanges the rigging and the corigging. We do this by giving a recognition theorem for B(∞) using the ⁎-involution. As a consequence, we also characterize

    更新日期:2021-01-14
  • On irreducible products of characters
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Gabriel Navarro; Pham Huu Tiep

    We study the problem when the product of two non-linear Galois conjugate characters of a finite group are irreducible. We also prove new results on irreducible tensor products of cross-characteristic Brauer characters of quasisimple groups of Lie type.

    更新日期:2021-01-14
  • Cohomology of bimultiplicative local systems on unipotent groups
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Prashant Arote; Tanmay Deshpande

    Let U1,U2 be connected commutative unipotent algebraic groups defined over an algebraically closed field k of characteristic p>0 and let L be a bimultiplicative Q‾ℓ-local system on U1×U2. In this paper we will study the Q‾ℓ-cohomology Hc⁎(U1×U2,L), which turns out to be supported in only one degree. We will construct a finite Heisenberg group Γ which naturally acts on Hc⁎(U1×U2,L) as an irreducible

    更新日期:2021-01-14
  • On cluster categories of weighted projective lines with at most three weights
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    Changjian Fu; Shengfei Geng

    Let X be a weighted projective line and CX the associated cluster category. It is known that CX can be realized as a generalized cluster category of quiver with potential. In this note, under the assumption that X has at most three weights or is of tubular type, we prove that if the generalized cluster category C(Q,W) of a Jacobi-finite non-degenerate quiver with potential (Q,W) shares a 2-CY tilted

    更新日期:2021-01-14
  • Affine commutative-by-finite Hopf algebras
    J. Algebra (IF 0.745) Pub Date : 2021-01-14
    K.A. Brown; M. Couto

    The objects of study in this paper are Hopf algebras H which are finitely generated algebras over an algebraically closed field and are extensions of a commutative Hopf algebra A by a finite dimensional Hopf algebra H‾:=H/A+H, where A+ is the augmentation ideal of A. Basic structural and homological properties are recalled and classes of examples are listed. A structure theorem is proved when (⁎) H‾

    更新日期:2021-01-14
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