In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties under homomorphic image and their transfer to various contexts of constructions such as direct product, trivial ring extension and amalgamated duplication of a ring

Rings in which each finitely generated right ideal is automorphism-invariant (rightfa-rings) are shown to be isomorphic to a formal matrix ring. Among other results it is also shown that (i) if R is a right nonsingular ring and n>1 is an integer, then R is a right self injective regular ring if and only if the matrix ring 𝕄n(R) is a right fa-ring, if and only if 𝕄n(R) is a right automorphism-invariant

In 2004, Shestakov and Umirbaev proved that the Nagata automorphism of the polynomial algebra in three variables is wild. We fix a ℤ-grading on this algebra and consider graded-wild automorphisms, i.e. such automorphisms that cannot be decomposed onto elementary automorphisms respecting the grading. We describe all gradings allowing graded-wild automorphisms.

We study canonical bases of a subalgebra A=𝕂[[f1,…,fs]]⊆𝕂[[x1,…,xn]] over a field 𝕂, and we associate with A a fan called the canonical fan of A. This generalizes the notion of the standard fan of an ideal.

In this paper, we mainly investigate the class-preserving Coleman automorphisms of finite groups whose Sylow 2-subgroups are semidihedral. We prove that if G is a finite solvable group with semidihedral Sylow 2-subgroups, then Outc(G)∩OutCol(G) is a 2′-group and therefore G satisfies the normalizer property. As some applications of this result, we also investigate the normalizer property of the following

We introduce a family of posets which generate Lie poset subalgebras of \(A_{n-1}=\mathfrak {sl}(n)\) whose index can be realized topologically. In particular, if \(\mathcal {P}\) is such a toral poset, then it has a simplicial realization which is homotopic to a wedge sum of d one-spheres, where d is the index of the corresponding type-A Lie poset algebra \(\mathfrak {g}_A(\mathcal {P})\). Moreover

Let G be a generalized Baumslag–Solitar group, and let C be a class of groups containing at least one non-trivial group and closed under taking subgroups, extensions, and Cartesian products of the form ∏y∈YXy, where X, Y∈C and Xy is an isomorphic copy of X for every y∈Y. We give a criterion for G to be residually a C-group provided C consists only of periodic groups. We also prove that G is residually

We prove that the isomorphism type of the subrack lattice of a finite group determines the nilpotence class. We analyze the problem of estimating the orders of the group elements corresponding to the atoms of the subrack lattice. As a result, we show that the subrack lattice determines p-nilpotence of the group if a certain condition is met.

A Correction to this paper has been published: https://doi.org/10.1007/s00006-020-01074-8

At present, the conventional finite element method (FEM) still has some defects for solving acoustic problems governed by the Helmholtz equation. Owing to the numerical dispersion error, the standard FEM always fails to provide sufficiently satisfactory results in high frequency range. To cure this drawback, an enriched finite element method (E-FEM) with interpolation cover functions is presented to

Abstract In this paper, we derive pre-anti-flexible algebras structures in term of zero weight’s Rota-Baxter operators, built underlying left-symmetric algebras, view pre-anti-flexible algebras as a splitting of anti-flexible algebras, introduce pre-anti-flexible bialgebras and establish its equivalences among matched pair of anti-flexible algebras and matched pair of pre-anti-flexible algebras. Special

Equivalence classes of Niho bent functions are in one-to-one correspondence with equivalence classes of ovals in a projective plane. Since a hyperoval can produce several ovals, each hyperoval is associated with several inequivalent Niho bent functions. For all known types of hyperovals we described the equivalence classes of the corresponding Niho bent functions. For some types of hyperovals the number

Two classes of determinants with their matrix entries being polynomial differences are evaluated in closed product expressions. They extend with many free parameters the Vandermonde-like determinant identities associated with the classical root systems.

A complex square matrix is a ray pattern matrix if each of its nonzero entries has modulus 1. A ray pattern matrix naturally corresponds to a weighted-digraph. A ray pattern matrix A is ray nonsingular if for each entry-wise positive matrix K, A∘K is nonsingular. A random model of ray pattern matrices with order n is introduced, where a uniformly random ray pattern matrix B is defined to be the adjacency

Abstract:Let $G$ be a connected reductive group defined over a finite field $\mathbf {F}_q$ and let $L$ be a Levi subgroup (defined over $\mathbf {F}_q$) of a parabolic subgroup $P$ of $G$. We define a linear map from class functions on $L(\mathbf {F}_q)$ to class functions on $G(\mathbf {F}_q)$. This map is independent of the choice of $P$. We show that for large $q$ this map coincides with the known

In this paper, we give the definition of unstable topological entropy in mean u-metrics (the mean metrics in the unstable manifold) for partially hyperbolic systems. By establishing the Katok's entropy formula of unstable metric entropy in mean u-metrics, we prove that the new unstable topological entropy is equal to the unstable topological entropy defined in Bowen u-metrics (the Bowen metrics in

For a class of piecewise convex maps f on the interval [0,1], we show that f has a unique absolutely continuous invariant probability measure μ with exponential decay of correlations, and we also present the explicit upper bounds on the rate. Moreover, we show the exponential loss of memory for a sequential dynamical system consisting of piecewise convex maps.

In this paper we review existing hard-decision decoding algorithms for product codes along with different post-processing techniques used in conjunction with the iterative decoder for product codes. We improve the decoder by Reddy and Robinson and use it to create a new post-processing technique. The performance of this new post-processing technique is evaluated through simulations, and these suggest

Abstract In this work we study some structural properties of the group ηq(G,H), q a non-negative integer, which is an extension of the q-tensor product G⊗qH, where G and H are normal subgroups of some group L. We establish by simple arguments some closure properties of ηq(G,H) when G and H belong to certain Schur classes. This extends similar results concerning the case q = 0 found in the literature

Abstract We refine the Morgan’s work on mixed Hodge structures on Sullivan’s 1-minimal models by using non-abelian Hodge theory. As an application, we give explicit representatives of real unipotent variations of mixed Hodge structures over compact Kähler manifolds.

Abstract Let R be a commutative ring with nonzero identity. Yassine et al. defined the concept of 1-absorbing prime ideals as follows: a proper ideal I of R is said to be a 1-absorbing prime ideal if whenever xyz∈I for some nonunit elements x,y,z∈R, then either xy∈I or z∈I. We use the concept of 1-absorbing prime ideals to study those commutative rings in which every proper ideal is a product of 1-absorbing

Abstract The exterior degree d∧(G) of a finite group G is the probability that a pair (x, y) of elements x, y chosen uniformly at random in G satisfies x∧y=1∧, where ∧ is the operator of nonabelian exterior square G∧G and 1∧ neutral element in G∧G. The probability d(G) that two elements of G commute is related to d∧(G). Of course, d(G) = 1 iff G is abelian, but d∧(G)=1 iff G is cyclic, so we detect

We define and explore rack objects internal to categories with products. In demonstration, we classify the group-racks, and use homotopy to prove both existence and exclusion theorems for path-connected topological racks.

In this paper, we recall the geometric definition of the braid group by Emil Artin and we give a complete, elementary geometric/topological proof of the standard presentation of the braid group on n strings.

We study zero divisors whose components alternate strongly pairwise and construct oriented hexagons in the zero divisor graph of an arbitrary real Cayley–Dickson algebra. In case of the algebras of the main sequence, the zero divisor graph coincides with the orthogonality graph, and any hexagon can be extended to a double hexagon. We determine the multiplication table of the vertices of a double hexagon

The study of Reynolds algebras has its origin in the well-known work of O. Reynolds on fluid dynamics in 1895 and has since found broad applications. It also has close relationship with important linear operators such as algebra endomorphisms, derivations and Rota-Baxter operators. Many years ago, G. Birkhoff suggested an algebraic study of Reynolds operators, including the corresponding free algebras

Let Fq be a finite field with q elements, n≥2 a positive integer, V0 a n-dimensional vector space over Fq and T0 the set of all linear functionals from V0 to Fq. Let V=V0∖{0} and T=T0∖{0}. The linear functional graph of V0 dented by ϝ(V), is an undirected bipartite graph, whose vertex set V is partitioned into two sets as V=V∪T and two vertices v∈V and f∈T are adjacent if and only if f sends v to the

We investigate the size of the largest entry (in absolute value) in the inverse of certain Vandermonde matrices. More precisely, for every real b>1, let Mb(n) be the maximum of the absolute values of the entries of the inverse of the n×n matrix [bij]0≤i,j

Rays are classes of an equivalence relation on a module V over a supertropical semiring. They provide a version of convex geometry, supported by a ‘supertropical trigonometry’ and compatible with quasilinearity, in which the CS-ratio takes the role of the Cauchy–Schwarz inequality. CS-functions that emerge from the CS-ratio are a useful tool that helps to understand the variety of quasilinear stars

The proper power graph P∗(G) of a group G is the simple graph with non-trivial elements of G as vertices and two distinct elements are adjacent if and only if one is a power of the other. The aim of this paper is to find the structure and to compute the spectrum of the proper power graph of direct product of two finite groups G1 and G2, where at least one of G1 and G2 is an EPO group. Also we provide

In this paper, we focus on the extensions of the Bessel matrix function and the modified Bessel matrix function. We first introduce the extended Bessel matrix function and the extended modified Bessel matrix function of the first kind by using the extended Beta matrix function. Then we establish the integral representations, differentiation formula, and hypergeometric representation of such functions

Let S be an unramified regular local ring of mixed characteristic two and R the integral closure of S in a biquadratic extension of its quotient field obtained by adjoining roots of sufficiently general square free elements f,g∈S. Let S2 denote the subring of S obtained by lifting to S the image of the Frobenius map on S/2S. When at least one of f,g∈S2, we characterize the Cohen-Macaulayness of R and

In this paper, we introduce and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra that generalizes notions of a Rota-Baxter operator on a group and a Rota-Baxter operator of weight 1 on a Lie algebra. We show that every Rota-Baxter operator (of weight 1) on a Lie algebra g (resp., on a group G) can be uniquely extended to a Rota-Baxter operator on the universal enveloping algebra

We study the two dual notions of prime avoidance and prime absorbance. We generalize the classical prime avoidance lemma to radical ideals. A number of new criteria are provided for an abstract ring to be compactly packed (C.P., every set of primes satisfies avoidance) or properly zipped (P.Z., every set of primes satisfies absorbance). Special consideration is given to the interaction with chain conditions

We consider Donovan's conjecture in the context of blocks of groups G with defect group D and normal subgroups N◁G such that G=CD(D∩N)N, extending similar results for blocks with abelian defect groups. As an application we show that Donovan's conjecture holds for blocks with defect groups of the form Q8×C2n or Q8×Q8 defined over a discrete valuation ring.

We begin by recalling the role that weak proregularity of an ideal in a commutative ring has in derived completion and adic flatness. We also introduce the new concepts of idealistic and sequential derived completion, and prove a few results about them, including the fact that these two concepts agree iff the ideal is weakly proregular. Next we study the local nature of weak proregularity, and its

Let K be an algebraically closed field of characteristic zero and let KC〚x1,⋯,xe〛 be the ring of formal power series in several variables with exponents in a line free cone C. We consider irreducible polynomials f=yn+a1(x_)yn−1+⋯+an(x_) in KC〚x1,⋯,xe〛[y] whose roots are in KC〚x11n,⋯,xe1n〛. We generalize to these polynomials the theory of Abhyankar-Moh. In particular we associate with any such polynomial

Let V be a valuation domain and let E be a subset of V. For a rank-one valuation domain V, there is a characterization of when Int(E,V) is a Prüfer domain. For a general valuation domain V, we show that Int(E,V) is a Prüfer domain if and only if E is precompact, or there exists a rank-one prime ideal P of V and Int(E,VP) is a Prüfer domain. Then we show that the following statements are equivalent:

The main focus of this paper is on determining the highest non-vanishing local cohomology modules of ΩB/R,ΩB/V(ΩB/k) where R is either a complete regular local ring or a complete local normal domain with coefficient ring V (field k) and B is its integral closure in an algebraic extension of Q(R). Similar problem is also studied over a normal domain R containing a field k of characteristic 0. In this

We define a class of numerical semigroups S, which we call Castelnuovo semigroups, and study the subvariety Mg,1S of Mg,1 consisting of marked smooth curves with Weierstrass semigroup S. We determine the number of irreducible components of these loci and determine their dimensions. Curves with these Weierstrass semigroups are always Castelnuovo curves, which provides the basic tool for our argument

For a partition λ of n∈N, let IλSp be the ideal of R=K[x1,…,xn] generated by all Specht polynomials of shape λ. In the previous paper, the second author showed that if R/IλSp is Cohen-Macaulay, then λ is either (n−d,1,…,1),(n−d,d), or (d,d,1), and the converse is true if char(K)=0. In this paper, we compute the Hilbert series of R/IλSp for λ=(n−d,d) or (d,d,1). Hence, we get the Castelnuovo-Mumford

We find a condition on the underlying graph of an Artin group that fully determines if it is subgroup separable. As a consequence, an Artin group is subgroup separable if and only if it can be obtained from the irreducible spherical Artin groups of ranks 1 and 2 via a finite sequence of free products and direct products with the infinite cyclic group. This result generalizes the Metaftsis-Raptis criterion

In this paper we verify Navarro's refinement of the McKay conjecture for quasi-simple groups of Lie type in their defining characteristic. Navarro's refinement takes into account the action of specific Galois automorphisms on the characters present in the McKay conjecture [13]. Our proof of this case of the conjecture relies on a character correspondence constructed by Maslowski in [12]. Building on

Sets of zero-dimensional ideals in the polynomial ring k[x,y] that share the same leading term ideal with respect to a given term ordering are known to be affine spaces called Gröbner cells. Conca-Valla and Constantinescu parametrize such Gröbner cells in terms of certain canonical Hilbert-Burch matrices for the lexicographical and degree-lexicographical term orderings, respectively. In this paper

Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent two-component links is odd, and Kazakov and Korablev proved that for every spatial complete graph with arbitrary number of vertices greater than six, the sum of the linking numbers over all of the constituent two-component Hamiltonian links is even. In this paper

Abstract We extend characterizations of inverses along an element to (b, c)-inverses. It is proved that if an element a in a semigroup S is both (b, c)-invertible and (c, b)-invertible for some b,c∈S, then abac,acab,caba,baca are group invertible, and bac(abac)♯=ba(caba)♯c=b(acab)♯ac=(baca)♯bac is the (b, c)-inverse of a, cab(acab)♯=ca(baca)♯b=c(abac)♯ab=(caba)♯cab is the (c, b)-inverse of a. Moreover

Abstract Let D1 and D2 be fixed diagonalizable matrices of Mn(C), the algebra of n × n matrices over the complex numbers, such that D1 and D2 have the same eigenvalues, counting multiplicities. In this paper, we characterize bijective linear maps f:Mn(C)→Mn(C) satisfying f(A)f(B)=D2 whenever AB=D1. It will be shown that f must be a scalar times an automorphism whenever D1 and D2 contain a zero eigenvalue

Abstract This article explores a generalization of the algebraic theory of formal languages. Having, as starting point, the work of T. Colcombet on cost functions and stabilization monoids, and of Daviaud et al. on stabilization algebras, this class of algebras is extended to ω♯-algebras and ω♯-automata are also introduced. The equality problem for order ideals (of free ω♯-algebras) recognized by finite

A Correction to this paper has been published: https://doi.org/10.1007/s10711-015-0119-z

We study some properties of formal local cohomology modules ℱ𝔞i(M) in Serre subcategories. As a consequence, we obtain some results on the minimax modules. We also describe the sets CosR(ℱ𝔞i(M)) and CoassR(ℱ𝔞i(M)).

A first aim of this paper is to give sufficient conditions on left non-degenerate bijective set-theoretic solutions of the Yang–Baxter equation so that they are non-degenerate. In particular, we extend the results on involutive solutions obtained by Rump in A decomposition theorem for square-free unitary solutions of the quantum Yang–Baxter equation, Adv. Math. 193 (2005) 40–55, https://doi.org/10

The Bochner–Schoenberg–Eberlein (BSE)-property on commutative Banach algebras is a property related to multiplier algebras of Banach algebras. In this paper, we answer the problem (12) raised by Javanshiri and Nemati in [Amalgamated duplication of the Banach algebra 𝔄 along a 𝔄-bimodule 𝒜, J. Algebra Appl.17(9) (2018) 1850169-1–1850169-21]. In this paper, under certain conditions, we show that the

In this paper, we prove that if R is a local ring of dimension d,d≥2 and 1d!∈R then the group Umd+1(R[X])Ed+1(R[X]) has no k-torsion, provided kR=R. We also prove that if R is a regular ring of dimension d,d≥2 and 1d!∈R such that Ed+1(R) acts transitively on Umd+1(R) then Ed+1(R[X]) acts transitively on Umd+1(R[X]).

In this paper, we study the behavior of endomorphism rings of indecomposable (uniform) quasi-injective modules. A very natural question here is, for a morphism f:A→B, with A,B indecomposable (uniform) quasi-injective right R-modules, and g:E(A)→E(B) an extension of f where E(−) denotes the injective hull, what is the relation between kernels of f and g, their monogeny classes and their upper parts

Minimal linear codes form a special class of linear codes that have important applications in secret sharing and secure two-party computation. These codes are characterized by the property that linearly independent codewords do not cover each other. Denoting by \(w_{\mathrm {min}}\) and \(w_{\mathrm {max}}\) the minimum and maximum weights of a binary code, respectively, such codes can be designed

In this paper, we propose an efficient method to find lightweight involutory MDS matrices. To obtain involutory matrices, we give a necessary and sufficient condition for judging the involutory MDS property and propose a search method. For the \(n\times n\) involutory MDS matrices over \({\mathbb {F}}_{2^m}\), the amount of computation is reduced from \(2^{mn^2}\) to \(2^{(mn^2)/2}\). Especially, we

Abstract The purpose of this short note is to correct an error which appears in the literature concerning Leibniz algebras L: namely, that N(L/I)=N(L)/I where N(L) is the nilradical of L and I is the Leibniz kernel.

We study the existence of a Batalin-Vilkovisky differential on the complete cohomology ring of a Frobenius algebra. We construct a Batalin-Vilkovisky differential on the complete cohomology ring in the case of Frobenius algebras with diagonalizable Nakayama automorphisms.

On construit des homomorphismes entre l'algèbre de Hecke générique Hn(q) de type A et l'algèbre de Hecke affine dégénérée DH(Sn) au moyen d'un élément générique Rqν(X,S) qui satisfait la relation de Hecke quadratique. Par spécialisation des DH(Sn) avec les éléments de Jucys-Murphy associés au groupe symétrique Sn, on obtient des isomorphismes explicites, après extension des scalaires à C(q), entre