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  • 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
  • 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
  • A note on a question of Markman
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-07
    Shengyuan Huang

    Let F be a vector bundle on a complex projective algebraic variety X. If F deforms along a first order deformation of X, its Mukai vector remains of Hodge type along this deformation. We prove an analogous statement for all polyvector fields, not only for those in H1(X,TX) corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue

    更新日期:2021-01-13
  • Supercharacter theories for Sylow p-subgroups of the Ree groups
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-13
    Yujiao Sun

    We determine a supercharacter theory for Sylow p-subgroups G2syl2(32m+1) of the Ree groups G22(32m+1), calculate the conjugacy classes of G2syl2(32m+1), and establish the character table of G2syl2(3).

    更新日期:2021-01-13
  • Homology of categories via polygraphic resolutions
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-12
    Léonard Guetta

    In this paper, we prove that the polygraphic homology of a small category, defined in terms of polygraphic resolutions in the category ωCat of strict ω- categories, is naturally isomorphic to the homology of its nerve, thereby extending a result of Lafont and Métayer. Along the way, we investigate homotopy colimits with respect to the Folk model structure and deduce a theorem which formally resembles

    更新日期:2021-01-12
  • Composing Dinatural Transformations: Towards a Calculus of Substitution
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-12
    Guy McCusker; Alessio Santamaria

    Dinatural transformations, which generalise the ubiquitous natural transformations to the case where the domain and codomain functors are of mixed variance, fail to compose in general; this has been known since they were discovered by Dubuc and Street in 1970. Many ad hoc solutions to this remarkable shortcoming have been found, but a general theory of compositionality was missing until Petrić, in

    更新日期:2021-01-12
  • Higher Codimension Cycles on the Hilbert Scheme of Three Points on the Projective Plane
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-12
    Tim Ryan; Alexander Stathis

    In this paper, we study the higher codimensional cycle structure of the Hilbert scheme of three points in the projective plane. In particular, we compute all Chern/Segre classes of all tautological bundles on it and compute the nef (effective) cones of cycles in codimensions 2 and 3 (dimensions 2 and 3).

    更新日期:2021-01-12
  • Jordan blocks of nilpotent elements in some irreducible representations of classical groups in good characteristic
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-11
    Mikko Korhonen

    Let G be a classical group with natural module V and Lie algebra g over an algebraically closed field K of good characteristic. For rational irreducible representations f:G→GL(W) occurring as composition factors of V⊗V⁎, ∧2(V), and S2(V), we describe the Jordan normal form of df(e) for all nilpotent elements e∈g. The description is given in terms of the Jordan block sizes of the action of e on V⊗V⁎

    更新日期:2021-01-11
  • Monadic cointegrals and applications to quasi-Hopf algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-11
    Johannes Berger; Azat M. Gainutdinov; Ingo Runkel

    For C a finite tensor category we consider four versions of the central monad, A1,…,A4 on C. Two of them are Hopf monads, and for C pivotal, so are the remaining two. In that case all Ai are isomorphic as Hopf monads. We define a monadic cointegral for Ai to be an Ai-module morphism 1→Ai(D), where D is the distinguished invertible object of C. We relate monadic cointegrals to the categorical cointegral

    更新日期:2021-01-11
  • Construction of the circle in UniMath
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-11
    Marc Bezem; Ulrik Buchholtz; Daniel R. Grayson; Michael Shulman

    We show that the type TZ of Z-torsors has the dependent universal property of the circle, which characterizes it up to a unique homotopy equivalence. The construction uses Voevodsky's Univalence Axiom and propositional truncation, yielding a stand-alone construction of the circle not using higher inductive types.

    更新日期:2021-01-11
  • Linear strands of edge ideals of multipartite uniform clutters
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-09
    Amin Nematbakhsh

    We construct the first linear strand of the minimal free resolutions of edge ideals of d-partite d-uniform clutters. We show that the first linear strand of such ideals are supported on relative simplicial complexes. In the case that the edge ideals of such clutters have linear resolutions, we give an explicit and surprisingly simple description of their minimal free resolutions, generalizing known

    更新日期:2021-01-10
  • Local Duality for Connected Z-algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-08
    I. Mori; A. Nyman

    We develop basic homological machinery for Z-algebras in order to prove a version of local duality for Ext-finite connected Z-algebras. As an application, we compare two notions of regularity for such algebras.

    更新日期:2021-01-10
  • Epsilon multiplicity for graded algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2021-01-07
    Suprajo Das

    The notion of ε-multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. In this article we show that the relative ε-multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's

    更新日期:2021-01-07
  • Partial actions and proper extensions of two-sided restriction semigroups
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-11
    Mikhailo Dokuchaev; Mykola Khrypchenko; Ganna Kudryavtseva

    We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study several classes of partial actions of two-sided restriction semigroups that generalize partial actions of monoids and of inverse semigroups. We establish an adjunction

    更新日期:2021-01-05
  • Trace ideals of canonical modules, annihilators of Ext modules, and classes of rings close to being Gorenstein
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-14
    Hailong Dao; Toshinori Kobayashi; Ryo Takahashi

    In this note we study trace ideals of canonical modules. Characterizations of the trace ideals in terms of annihilators of certain Ext modules are given. We apply our results to study many classes of rings close to being Gorenstein that appear in recent literature. We discuss the behavior of near Gorensteinness, introduced by Herzog, Hibi and Stamate, under reductions by regular sequences. A nearly

    更新日期:2021-01-05
  • Dynamical combinatorics and torsion classes
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-16
    Emily Barnard; Gordana Todorov; Shijie Zhu

    For finite semidistributive lattices the map κ gives a bijection between the sets of completely join-irreducible elements and completely meet-irreducible elements. Here we study the κ-map in the context of torsion classes. It is well-known that the lattice of torsion classes for an artin algebra is semidistributive, but in general it is far from finite. We show the κ-map is well-defined on the set

    更新日期:2020-12-30
  • The 2-minimal subgroups of symplectic groups
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-10
    Chris Parker; Peter Rowley

    For a finite group G, a subgroup P of G is 2-minimal if B

    更新日期:2020-12-29
  • Infinite families of cyclotomic function fields with any prescribed class group rank
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-29
    Jinjoo Yoo; Yoonjin Lee

    We prove the existence of the maximal real subfields of cyclotomic extensions over the rational function field k=Fq(T) whose class groups can have arbitrarily large ℓn-rank, where Fq is the finite field of prime power order q. We prove this in a constructive way: we explicitly construct infinite families of the maximal real subfields k(Λ)+ of cyclotomic function fields k(Λ) whose ideal class groups

    更新日期:2020-12-29
  • Multi-quadratic p-rational number fields
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-16
    Y. Benmerieme; A. Movahhedi

    For each odd prime p, we prove the existence of infinitely many real quadratic fields which are p-rational. Explicit imaginary and real bi-quadratic p-rational fields are also given for each prime p. Using a recent method developed by Greenberg, we deduce the existence of Galois extensions of Q with Galois group isomorphic to an open subgroup of GLn(Zp), for n=4 and n=5 and at least for all the primes

    更新日期:2020-12-23
  • Equivalences of graded fusion categories
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-16
    Cain Edie-Michell

    We further the techniques developed by Etingof, Nikshych, and Ostrik in [7] to classify the C-based equivalences between two G-graded extensions of C, in terms of cohomological data. As a warm up for the proof of our classification result we reprove the classification of graded extensions of a fusion category, making extensive use of graphical calculus. We end by providing several practical applications

    更新日期:2020-12-21
  • Quivers supporting twisted Calabi-Yau algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-14
    Jason Gaddis; Daniel Rogalski

    We consider graded twisted Calabi-Yau algebras of dimension 3 which are derivation-quotient algebras of the form A=kQ/I, where Q is a quiver and I is an ideal of relations coming from taking partial derivatives of a twisted superpotential on Q. We define the type (M,P,d) of such an algebra A, where M is the incidence matrix of the quiver, P is the permutation matrix giving the action of the Nakayama

    更新日期:2020-12-21
  • On the orders of vanishing elements of finite groups
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-11
    Sesuai Y. Madanha

    Let G be a finite group and p be a prime. Let Vo(G) denote the set of the orders of vanishing elements, Vop(G) be the subset of Vo(G) consisting of those orders of vanishing elements divisible by p and Vop′(G) be the subset of Vo(G) consisting of those orders of vanishing elements not divisible by p. Dolfi, Pacifi, Sanus and Spiga proved that if a is not a p-power for all a∈Vo(G), then G has a normal

    更新日期:2020-12-18
  • Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type (C1∨,C1)
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-11
    Hau-Wen Huang

    Assume that F is an algebraically closed field with characteristic zero. The universal Racah algebra ℜ is a unital associative F-algebra defined by generators and relations. The generators are A,B,C,D and the relations state that[A,B]=[B,C]=[C,A]=2D and each of[A,D]+AC−BA,[B,D]+BA−CB,[C,D]+CB−AC is central in ℜ. The universal additive DAHA (double affine Hecke algebra) H of type (C1∨,C1) is a unital

    更新日期:2020-12-18
  • Singularity categories of Gorenstein monomial algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-11
    Ming Lu; Bin Zhu

    In this paper, we consider the singularity category Dsg(modA) and the Z-graded singularity category Dsg(modZA) for a Gorenstein monomial algebra A. Firstly, for a positively graded 1-Gorenstein algebra, we prove that its Z-graded singularity category admits silting objects. Secondly, for A=KQ/I being a Gorenstein monomial algebra, we prove that Dsg(modZA) has tilting objects. As a consequence, Dsg(modZA)

    更新日期:2020-12-18
  • On some combinatorial properties of generalized cluster algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-10
    Peigen Cao; Fang Li

    In this paper, we prove some combinatorial results on generalized cluster algebras. To be more precise, we prove that (i) the seeds of a generalized cluster algebra A(S) whose clusters contain particular cluster variables form a connected subgraph of the exchange graph of A(S); (ii) there exists a bijection from the set of cluster variables of a generalized cluster algebra to the set of cluster variables

    更新日期:2020-12-18
  • Recollements of derived categories I: Construction from exact contexts
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-10
    Hongxing Chen; Changchang Xi

    A new method is established to construct recollements of derived categories of rings from exact contexts and noncommutative tensor products. This method is applicable to a large variety of situations, including Milnor squares, localizations, ring extensions and ring epimorphisms.

    更新日期:2020-12-18
  • An SOS counterexample to an inequality of symmetric functions
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-14
    Alexander Heaton; Isabelle Shankar

    It is known that differences of symmetric functions corresponding to various bases are nonnegative on the nonnegative orthant exactly when the partitions defining them are comparable in dominance order. The only exception is the case of homogeneous symmetric functions where it is only known that dominance of the partitions implies nonnegativity of the corresponding difference of symmetric functions

    更新日期:2020-12-18
  • On the k-torsion of the module of differentials of order n of hypersurfaces
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-09
    Hernán de Alba; Daniel Duarte

    We characterize the k-torsion freeness of the module of differentials of order n of a point of a hypersurface in terms of the singular locus of the corresponding local ring.

    更新日期:2020-12-16
  • On MacLane-Vaquié key polynomials
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-10
    Josnei Novacoski

    One of the main goals of this paper is to present the relation between limit key polynomials and MacLane-Vaquié limit key polynomials. This is a continuation of the work started in [3], where the equivalent result for key polynomials (which are not limit) is proved. Moreover, we present a result (Theorem 1.1) that generalizes various results in the literature.

    更新日期:2020-12-16
  • Verschiebung maps among K-groups of truncated polynomial algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-04
    Ryo Horiuchi

    Let p be a prime number, and let A be a ring in which p is nilpotent. In this paper, we consider the mapsKq+1(A[x]/(xm),(x))→Kq+1(A[x]/(xmn),(x)), induced by the ring homomorphism A[x]/(xm)→A[x]/(xmn), x↦xn. We evaluate these maps, up to extension, for general A in terms of topological Hochschild homology, and for regular Fp-algebras A, in terms of groups of de Rham-Witt forms. After the evaluation

    更新日期:2020-12-09
  • THH and TC are (very) far from being homotopy functors
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-07
    Elden Elmanto

    We compute the A1-localization of several invariants of schemes namely, topological Hochschild homology (THH), topological cyclic homology (TC) and topological periodic cyclic homology (TP). This procedure is quite brutal and kills the completed versions of most of these invariants. The main ingredient for the vanishing statements is the vanishing of A1-localization of de Rham cohomology (and, eventually

    更新日期:2020-12-09
  • Lower-bounded and grading-restricted twisted modules for affine vertex (operator) algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-12-04
    Yi-Zhi Huang

    We apply the construction of the universal lower-bounded generalized twisted modules by the author to construct universal lower-bounded and grading-restricted generalized twisted modules for affine vertex (operator) algebras. We prove that these universal twisted modules for affine vertex (operator) algebras are equivalent to suitable induced modules of the corresponding twisted affine Lie algebra

    更新日期:2020-12-09
  • Automorphisms of finitely generated relatively free bicommutative algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-18
    Ivan Shestakov; Zerui Zhang

    Automorphisms of free bicommutative algebras over an arbitrary field are studied. Wild automorphisms are constructed in two-generated and three-generated free bicommutative algebras. Moreover, for any n≥2, a wild automorphism is constructed in the n-generated free associative bicommutative algebra which is not stably tame and can not be lifted to an automorphism of the n-generated free bicommutative

    更新日期:2020-11-27
  • Higher level affine Schur and Hecke algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-10-02
    Ruslan Maksimau; Catharina Stroppel

    We define a higher level version of the affine Hecke algebra and prove that, after completion, this algebra is isomorphic to a completion of Webster's tensor product algebra of type A. We then introduce a higher level version of the affine Schur algebra and establish, again after completion, an isomorphism with the quiver Schur algebra. An important observation is that the higher level affine Schur

    更新日期:2020-11-27
  • Toric degenerations of flag varieties from matching field tableaux
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-16
    Oliver Clarke; Fatemeh Mohammadi

    We present families of tableaux which interpolate between the classical semi-standard Young tableaux and matching field tableaux. Algebraically, this corresponds to SAGBI bases of Plücker algebras. We show that each such family of tableaux leads to a toric ideal, that can be realized as initial of the Plücker ideal, hence a toric degeneration for the flag variety.

    更新日期:2020-11-26
  • Toric co-Higgs sheaves
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-09
    Klaus Altmann; Frederik Witt

    We characterise and investigate co-Higgs sheaves and associated algebraic and combinatorial invariants on toric varieties. In particular, we compute explicit examples.

    更新日期:2020-11-21
  • Triples of rational points on the Hermitian curve and their Weierstrass semigroups
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-18
    Gretchen L. Matthews; Dane Skabelund; Michael Wills

    In this paper, we study configurations of three rational points on the Hermitian curve over Fq2 and classify them according to their Weierstrass semigroups. For q>3, we show that the number of distinct semigroups of this form is equal to the number of positive divisors of q+1 and give an explicit description of the Weierstrass semigroup for each triple of points studied. To do so, we make use of two-point

    更新日期:2020-11-21
  • On sum of squares certificates of non-negativity on a strip
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-19
    Paula Escorcielo; Daniel Perrucci

    In [6], Murray Marshall proved that every f∈R[X,Y] non-negative on the strip [0,1]×R can be written as f=σ0+σ1X(1−X) with σ0,σ1 sums of squares in R[X,Y]. In this work, we present a few results concerning this representation in particular cases. First, under the assumption degY⁡f≤2, by characterizing the extreme rays of a suitable cone, we obtain a degree bound for each term. Then, we consider the

    更新日期:2020-11-19
  • Universal localization of certain matrix rings
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-11
    Tyler B. Bowles; Dariusz M. Wilczyński

    The Cohn localization is a process of adjoining universal inverse morphisms to the category of R-modules over a noncommutative ring R. Finding specific models for universal localizations is, in general, difficult. For certain classes of rings, however, there exist constructions that are more accessible. We define such a class of rings, the generalized triangular matrix rings, and provide complete descriptions

    更新日期:2020-11-18
  • Tridiagonal pairs of q-Racah type and the q-tetrahedron algebra
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-11
    Paul Terwilliger

    Let F denote a field, and let V denote a vector space over F with finite positive dimension. We consider an ordered pair of F-linear maps A:V→V and A⁎:V→V such that (i) each of A,A⁎ is diagonalizable; (ii) there exists an ordering {Vi}i=0d of the eigenspaces of A such that A⁎Vi⊆Vi−1+Vi+Vi+1 for 0≤i≤d, where V−1=0 and Vd+1=0; (iii) there exists an ordering {Vi⁎}i=0δ of the eigenspaces of A⁎ such that

    更新日期:2020-11-18
  • Covering numbers of commutative rings
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-09
    Eric Swartz; Nicholas J. Werner

    A cover of a unital, associative (not necessarily commutative) ring R is a collection of proper subrings of R whose set-theoretic union equals R. If such a cover exists, then the covering number σ(R) of R is the cardinality of a minimal cover, and a ring R is called σ-elementary if σ(R)<σ(R/I) for every nonzero two-sided ideal I of R. In this paper, we show that if R has a finite covering number, then

    更新日期:2020-11-18
  • On the central geometry of nonnoetherian dimer algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-01
    Charlie Beil

    Let Z be the center of a nonnoetherian dimer algebra on a torus. Although Z itself is also nonnoetherian, we show that it has Krull dimension 3, and is locally noetherian on an open dense set of Max Z. Furthermore, we show that the reduced center Z/nilZ is depicted by a Gorenstein singularity, and contains precisely one closed point of positive geometric dimension.

    更新日期:2020-11-18
  • Nombre de composantes connexes d'une variete reelle et R−places
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-17
    Danielle Gondard-Cozette

    Le but de cet article est de rassembler des résultats et des questions concernant un objet mal connu mais souvent utile, les R−places, et de fournir les références correspondantes. Nous commençons par rappeler les notions de base, puis présentons quelques résultats de géométrie réelle obtenus grâce aux R−places. En particulier le théorème 14 donne explicitement, en termes de corps des fonctions de

    更新日期:2020-11-17
  • On signed p-Kostka matrices
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-09
    Eugenio Giannelli; Kay Jin Lim

    We show that the signed p-Kostka numbers depend just on p-Kostka numbers and the multiplicities of projective indecomposable modules in certain signed Young permutation modules. We then examine the signed p-Kostka number k(α|β),(λ|pμ) in the case when |β|=p|μ|. This allows us to explicitly describe the multiplicities of direct summands of a signed Young permutation module lying in the principal block

    更新日期:2020-11-12
  • Residual coordinates over one-dimensional rings
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-09
    M'hammed El Kahoui; Najoua Essamaoui; Mustapha Ouali

    Given a noetherian ring R and n≥2, it is well-known that residual coordinates of the polynomial algebra R[n] are m-stable coordinates for some m≥1, that is they become coordinates in the larger polynomial algebra R[n+m]. In this paper we prove that, over a large class of noetherian one-dimensional rings, m=1 is enough. This includes affine algebras over an algebraically closed field as well as noetherian

    更新日期:2020-11-12
  • Almost complete intersection binomial edge ideals and their Rees algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-09
    A.V. Jayanthan; Arvind Kumar; Rajib Sarkar

    Let G be a simple graph on n vertices and JG denote the binomial edge ideal of G in the polynomial ring S=K[x1,…,xn,y1,…,yn]. In this article, we compute the second graded Betti numbers of JG, and we obtain a minimal presentation of it when G is a tree or a unicyclic graph. We classify all graphs whose binomial edge ideals are almost complete intersection, prove that they are generated by a d-sequence

    更新日期:2020-11-12
  • The algebraic and geometric classification of nilpotent terminal algebras
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-10
    Ivan Kaygorodov; Mykola Khrypchenko; Yury Popov

    We give algebraic and geometric classifications of 4-dimensional complex nilpotent terminal algebras. Specifically, we find that, up to isomorphism, there are 41 one-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 18 two-parameter families of 4-dimensional nilpotent terminal (non-Leibniz) algebras, 2 three-parameter families of 4-dimensional nilpotent terminal (non-Leibniz)

    更新日期:2020-11-12
  • Fundamental groupoids for simplicial objects in Mal'tsev categories
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-06
    Arnaud Duvieusart

    We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and, moreover, a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois structure, and show that regular epimorphisms admit a relative monotone-light factorization system in the sense of Chikhladze. We also draw some comparison with

    更新日期:2020-11-12
  • Ext groups in the category of bimodules over a simple Leibniz algebra
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-10
    Jean Mugniery; Friedrich Wagemann

    In this article, we generalize Loday and Pirashvili's [11] computation of the Ext-category of Leibniz bimodules for a simple Lie algebra to the case of a simple (non Lie) Leibniz algebra. Most of the arguments generalize easily, while the main new ingredient is the Feldvoss-Wagemann's cohomology vanishing theorem for semi-simple Leibniz algebras.

    更新日期:2020-11-12
  • Uniqueness of uniform decompositions in exact categories
    J. Pure Appl. Algebra (IF 0.77) Pub Date : 2020-11-06
    Mustafa Kemal Berktaş; Septimiu Crivei; Fatma Kaynarca; Derya Keskin Tütüncü

    Two uniqueness theorems on uniform decompositions due to Krause, Diracca and Facchini are extended from abelian categories to weakly idempotent complete exact categories. We give applications to (quasi-)abelian categories, finitely accessible additive categories and exactly definable additive categories.

    更新日期:2020-11-12
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