共查询到20条相似文献,搜索用时 62 毫秒
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《Journal of Pure and Applied Algebra》2023,227(5):107279
In this paper we study the lower triangular matrix -algebra , where U and T are basic -algebras with enough idempotents and M is an U-T-bimodule where acts centrally. Moreover, we characterise in terms of U, T and M when, on one hand, the lower triangular matrix -algebra Λ is standardly stratified in the sense of [15]; and on the other hand, when Λ is locally bounded in the sense of Gabriel [10]. Finally, we also study several properties relating the projective dimensions in the categories of finitely generated modules , and . 相似文献
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A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. A graph G is a core if every endomorphism of G is an automorphism. Let be the finite field with q elements where q is a power of an odd prime number. The quadratic forms graph, denoted by where , has all quadratic forms on as vertices and two vertices f and g are adjacent whenever or 2. We prove that every is a pseudo-core. Further, when n is even, is a core. When n is odd, is not a core. On the other hand, we completely determine the independence number of . 相似文献
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Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on can be approximated uniformly on bounded sets by polyhedral norms and smooth norms, with arbitrary precision. We extend this result to more classes of spaces having uncountable symmetric bases, such as preduals of the ‘discrete’ Lorentz spaces , and certain symmetric Nakano spaces and Orlicz spaces. We also show that, given an arbitrary ordinal number α, there exists a scattered compact space K having Cantor–Bendixson height at least α, such that every equivalent norm on can be approximated as above. 相似文献
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Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring and we describe explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups. 相似文献
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《Discrete Mathematics》2022,345(8):112902
For a simple graph G, denote by n, , and its order, maximum degree, and chromatic index, respectively. A graph G is edge-chromatic critical if and for every proper subgraph H of G. Let G be an n-vertex connected regular class 1 graph, and let be obtained from G by splitting one vertex of G into two vertices. Hilton and Zhao in 1997 conjectured that must be edge-chromatic critical if , and they verified this when . In this paper, we prove it for . 相似文献
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《Discrete Mathematics》2022,345(8):112917
Let and denote the flow number and the circular flow number of a flow-admissible signed graph , respectively. It is known that for every unsigned graph G. Based on this fact, in 2011 Raspaud and Zhu conjectured that holds also for every flow-admissible signed graph . This conjecture was disproved by Schubert and Steffen using graphs with bridges and vertices of large degree. In this paper we focus on cubic graphs, since they play a crucial role in many open problems in graph theory. For cubic graphs we show that if and only if and if , then . We also prove that all pairs of flow number and circular flow number that fulfil these conditions can be achieved in the family of bridgeless cubic graphs and thereby disprove the conjecture of Raspaud and Zhu even for bridgeless signed cubic graphs. Finally, we prove that all currently known flow-admissible graphs without nowhere-zero 5-flow have flow number and circular flow number 6 and propose several conjectures in this area. 相似文献
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《Discrete Mathematics》2022,345(7):112893
In this paper, we study the Reconstruction Conjecture for finite simple graphs. Let Γ and be finite simple graphs with at least three vertices such that there exists a bijective map and for any , there exists an isomorphism . Then we define the associated directed graph with two kinds of arrows from the graphs Γ and , the bijective map f and the isomorphisms . By investigating the associated directed graph , we study when are the two graphs Γ and isomorphic. 相似文献
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Shai Shechter 《Journal of Pure and Applied Algebra》2019,223(10):4384-4425
Let be a complete discrete valuation ring with finite residue field of odd characteristic, and let G be a symplectic or special orthogonal group scheme over . For any let denote the ?-th principal congruence subgroup of . An irreducible character of the group is said to be regular if it is trivial on a subgroup for some ?, and if its restriction to consists of characters of minimal -stabilizer dimension. In the present paper we consider the regular characters of such classical groups over , and construct and enumerate all regular characters of , when the characteristic of is greater than two. As a result, we compute the regular part of their representation zeta function. 相似文献
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《Discrete Mathematics》2022,345(1):112631
For a graph , a total ordering L on V, and a vertex , let be the set of vertices for which there is a path from v to w whose length is 0, 1 or 2 and whose L-least vertex is w. The weak 2-coloring number of G is the least k such that there is a total ordering L on V with for all vertices . We improve the known upper bound on the weak 2-coloring number of planar graphs from 28 to 23. As the weak 2-coloring number is the best known upper bound on the star list chromatic number of planar graphs, this bound is also improved. 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