共查询到20条相似文献,搜索用时 15 毫秒
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Andrea Pasquali 《Journal of Pure and Applied Algebra》2019,223(8):3537-3553
If A and B are n- and m-representation finite k-algebras, then their tensor product is not in general -representation finite. However, we prove that if A and B are acyclic and satisfy the weaker assumption of n- and m-completeness, then Λ is -complete. This mirrors the fact that taking higher Auslander algebra does not preserve d-representation finiteness in general, but it does preserve d-completeness. As a corollary, we get the necessary condition for Λ to be -representation finite which was found by Herschend and Iyama by using a certain twisted fractionally Calabi–Yau property. 相似文献
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Wei Hu Xiu-Hua Luo Bao-Lin Xiong Guodong Zhou 《Journal of Pure and Applied Algebra》2019,223(3):1014-1039
We generalize the monomorphism category from quiver (with monomial relations) to arbitrary finite dimensional algebras by a homological definition. Given two finite dimension algebras A and B, we use the special monomorphism category to describe some Gorenstein projective bimodules over the tensor product of A and B. If one of the two algebras is Gorenstein, we give a sufficient and necessary condition for being the category of all Gorenstein projective bimodules. In addition, if both A and B are Gorenstein, we can describe the category of all Gorenstein projective bimodules via filtration categories. Similarly, in this case, we get the same result for infinitely generated Gorenstein projective bimodules. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(10):107074
For a commutative ring A we consider a related graph, , whose vertices are the unimodular rows of length 2 up to multiplication by units. We prove that is path-connected if and only if A is a -ring, in the terminology of P. M. Cohn. Furthermore, if denotes the clique complex of , we prove that is simply connected if and only if A is universal for . More precisely, our main theorem is that for any commutative ring A the fundamental group of is isomorphic to the group modulo the subgroup generated by symbols. 相似文献
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In this paper we construct a ring A which has annihilator condition (a.c.) and we show that neither nor has this property. This answers in negative a question asked by Hong, Kim, Lee and Nielsen. We also show that there is an algebra A which does not have annihilator condition while both and have this property. 相似文献
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Let be an abelian group. A finite multiset A over G is said to give a λ-fold factorization of G if there exists a multiset B over G such that each element of G occurs λ times in the multiset . In this article, restricting G to a cyclic group, we will provide sufficient conditions on a given multiset A under which the exact value or an upper bound of the minimum multiplicity λ of a factorization of G can be given by introducing a concept of ‘lcm-closure’. Furthermore, a couple of properties on a given factor A will be shown when A has a prime or prime power order (cardinality). A relation to multifold factorizations of the set of integers will be also glanced at a general perspective. 相似文献
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We construct a minimal free resolution of the semigroup ring in terms of minimal resolutions of and when is a numerical semigroup obtained by gluing two numerical semigroups and . Using our explicit construction, we compute the Betti numbers, graded Betti numbers, regularity and Hilbert series of , and prove that the minimal free resolution of has a differential graded algebra structure provided the resolutions of and possess them. We discuss the consequences of our results in small embedding dimensions. Finally, we give an extension of our main result to semigroups in . 相似文献
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《Discrete Mathematics》2021,344(12):112589
Let be the set of positive integers. For a nonempty set A of integers and every integer u, denote by the number of with such that . For a sequence S of positive integers, let be the counting function of S. The set is called a perfect difference set if for every positive integer u. In 2008, Cilleruelo and Nathanson (2008) [4] constructed dense perfect difference sets from dense Sidon sets. In this paper, as a main result, we prove that: let be an increasing function satisfying for any positive integer n, then for every Sidon set B and every function , there exists a set such that for every positive integer u and for all . 相似文献
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《Journal of Pure and Applied Algebra》2019,223(11):4966-4993
We introduce a type affine C analogue of the nil Temperley–Lieb algebra, in terms of generators and relations. We show that this algebra , which is a quotient of the positive part of a Kac–Moody algebra of type , has an easily described faithful representation as an algebra of creation and annihilation operators on particle configurations, reminiscent of the open TASEP model in statistical physics. The centre of consists of polynomials in a certain element Q, and is a free module of finite rank over its centre. We show how to localize by adjoining an inverse of Q, and prove that the resulting algebra is a full matrix ring over a ring of Laurent polynomials over a field. Although has wild representation type, over an algebraically closed field we can classify all the finite dimensional indecomposable representations of in which Q acts invertibly. 相似文献
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《Journal of Pure and Applied Algebra》2023,227(2):107179
Let D be an integral domain and let be a torsion-free, ≤-cancellative, subtotally ordered monoid. We show that the generalized power series ring is a Krull domain if and only if D is a Krull domain and S is a Krull monoid. 相似文献
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《Journal of Pure and Applied Algebra》2019,223(11):4592-4601
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Let R be a finite principal ideal ring and positive integers. In this paper, we study the matrix graph over R which is the graph whose vertices are matrices over R and two matrices A and B are adjacent if and only if . We show that this graph is a connected vertex transitive graph. The distance, diameter, independence number, clique number and chromatic number of this graph are also determined. This graph can be applied to study MRD codes over R. We obtain that a maximal independent set of the matrix graph is a maximum rank distance (MRD) code and vice versa. Moreover, we show the existence of linear MRD codes over R. 相似文献