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L—Fuzzy群的同态与同构及其性质 总被引:2,自引:1,他引:2
本文在L-fuzzy群的概念的基础上,用集合套概念定义了L-fuzzy群间的同态与同构。进而给出了它们的一些性质。最后,我们给出了L-fuzzy群的同态基本定理。 相似文献
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正则幂环的同态与同构 总被引:3,自引:0,他引:3
随着模糊数学的发展,各种代数结构的提升为得越来越重要,李洪兴教授在「1,2」中首次提出并研究了幂群及HX环,本文在文「3~6」的基础上深入讨论了幂环的一些性质,并在正则幂环中建立了几个同态与同构定理。 相似文献
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正则HX群的同态与同构 总被引:17,自引:2,他引:15
模糊数学的发展突出了集值映射的重要性,各种数学结构需要由论域向其幂集上提升,如序结构的提升,可测结构的提升,拓扑结构的提升等等。文[1]考虑了代数结构的提升问题,首次提出了HX群的概念,随后,文[2]又给出了HX环的定义,本文将在“正则”的条件下,研究HX群中的同态与同构形式。 相似文献
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本文研究了L—Fuzzy群的同态和同构,给出了它们的一些性质,并把群论中的同态定理和同构定理推广到L—Fuzzy群上 相似文献
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文(1)给出了L-Fuzzy群间的同态映射,满同态映射以及L-Fuzzy群的L-正规子群等概念。本文指出以上三种定义的不合理性,并给出它们的合理性定义。 相似文献
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余德民 《纯粹数学与应用数学》2016,32(1):14-18
构造了一类由三个基本元生成的无限维李代数.证明了这类无限维李代数是Virasoro-like李代数的推广.此外,研究了这类李子代数同构和同态. 相似文献
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We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups,and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre.We describe an algorithm that,given an arbitrary finite presentation of an automatic group Γ,will construct explicit finite models for the skeleta of K(Γ,1) and hence compute the integral homology and cohomology of Γ. 相似文献
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Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T ⊂ G, Cay(G, S) ≅ Cay(G, T) implies Sα = T for some α ∈ Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property; if all Cayley graphs of valency m are CI-graphs, then G is said to have the m-CI property. It is shown that every finite group of order greater than 2 has a nontrivial CI-graph, and all finite groups with the m-CI property and with the m-DCI property are characterized for small values of m. A general investigation is made of the structure of Sylow subgroups of finite groups with the m-DCI property and with the m-CI property for large values of m. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 21–31, 1998 相似文献
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The restricted homomorphism problem asks: given an input digraph G and a homomorphism g:G→Y, does there exist a homomorphism f:G→H? We prove that if H is hereditarily hard and YH, then is NP-complete. Since non-bipartite graphs are hereditarily hard, this settles in the affirmative a conjecture of Hell and Nešetřil. 相似文献
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Hamid Usefi 《Proceedings of the American Mathematical Society》2008,136(12):4125-4133
Let be a restricted Lie algebra with the restricted enveloping algebra over a perfect field of positive characteristic . The restricted isomorphism problem asks what invariants of are determined by . This problem is the analogue of the modular isomorphism problem for finite -groups. Bagiński and Sandling have given a positive answer to the modular isomorphism problem for metacyclic -groups. In this paper, we provide a positive answer to the restricted isomorphism problem in case is metacyclic and -nilpotent.
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Richard C. Brewster Jae-Baek Lee Benjamin Moore Jonathan A. Noel Mark Siggers 《Journal of Graph Theory》2020,94(3):398-420
We say that a graph strongly arrows a pair of graphs and write if any coloring of its edges with red and blue leads to either a red or a blue appearing as induced subgraphs of . The induced Ramsey number, , is defined as . We consider the connection between the induced Ramsey number for a pair of two connected graphs and the induced Ramsey number for multiple copies of these graphs , where denotes the pairwise vertex-disjoint union of copies of . It is easy to see that if , then . This implies that For several specific graphs, such as a path on three vertices vs a complete multipartite graph, a matching vs a complete graph, or a matching vs another matching, it is known that the above inequality is tight. On the other hand, the inequality is also strict for some graphs. However, even in the simplest case when is an edge and , it is not known for what and for what the above inequality is tight. We show that it is tight if is connected and is at least as large as the order of . In addition, we make further progress in determining induced Ramsey numbers for multiple copies of graphs, such as paths and triangles. 相似文献
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Nicole Lemire Vladimir L. Popov Zinovy Reichstein 《Journal of the American Mathematical Society》2006,19(4):921-967
The classical Cayley map, , is a birational isomorphism between the special orthogonal group SO and its Lie algebra , which is SO-equivariant with respect to the conjugating and adjoint actions, respectively. We ask whether or not maps with these properties can be constructed for other algebraic groups. We show that the answer is usually ``no", with a few exceptions. In particular, we show that a Cayley map for the group SL exists if and only if , answering an old question of LUNA.
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