共查询到20条相似文献,搜索用时 15 毫秒
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Bella V. Rozenblat 《Israel Journal of Mathematics》2002,128(1):355-379
The connections between first-order formulas over a completely simple semigroupC and corresponding formulas over its structure groupH are found in this paper. For the case of finite sandwich-matrix the criterion of decidability of the elementary theoryT(C) is established in terms of the elementary theory ofH in the enriched signature (Theorem 1). For the general case the criterion is established in terms of two-sorted algebraic
systems (Theorem 2). Sufficient conditions in terms ofH for decidability and for undecidability ofT(C) are outlined. Corollaries and examples are presented, among them an example of a completely simple semigroup with a finite
structure group and with undecidable elementary theory (Theorem 3). 相似文献
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Mario Petrich 《代数通讯》2013,41(8):3535-3553
Let S be a completely simple semigroup represented as a Rees matrix semigroup M(I,G,P) with normalized sandwich matrix P. On the congruence lattice C(S) of S we consider the relations T i, K and T r which identify congruences with the same left trace, kernel and right trace, respectively. These are equivalences whose classes are intervals. The upper and lower ends of these intervals induce the following operators on C(S) Tl, K, Tr, tl, k and tr .We construct here the semigroup generated by these operators as a homomorphic image of a semigroup given by generators and relations and demonstrate the minimality of the latter. 相似文献
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对完全0-单半群上的相容组条件进行简化,引入完全单半群上同余结的概念,并给出相容组与同余结的应用. 相似文献
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Roman S. Gigoń 《代数通讯》2018,46(11):4884-4890
We show that an E-inversive semigroup S has a completely simple kernel KS if and only if it contains a primitive idempotent (in that case, KS is the set-theoretic union of the groups eSe, where e is a primitive idempotent of S). Along the way, some equivalent conditions for a semigroup to be E-inversive are given. Moreover, some applications of the above theorem will be pointed out. 相似文献
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Algebra universalis - Completely simple semigroups form a variety if we consider them as algebras with multiplication and inversion. A near variety of idempotent generated completely simple... 相似文献
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Tamás Dékány 《Semigroup Forum》2014,89(3):600-608
An example of an extension of a completely simple semigroup \(U\) by a group \(H\) is given which cannot be embedded into the wreath product of \(U\) by \(H\) . On the other hand, every central extension of \(U\) by \(H\) is shown to be embeddable in the wreath product of \(U\) by \(H\) , and any extension of \(U\) by \(H\) is proved to be embeddable in a semidirect product of a completely simple semigroup \(V\) by \(H\) where the maximal subgroups of \(V\) are direct powers of those of \(U\) . 相似文献
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In this paper, the Cayley graphs of completely simple semigroups are investigated. The basic structure and properties of this
kind of Cayley graph are given, and a condition is given for a Cayley graph of a completely simple semigroup to be a disjoint
union of complete graphs. We also describe all pairs (S,A) such that S is a completely simple semigroup, A⊆S, and Cay (S,A) is a strongly connected bipartite Cayley graph. 相似文献
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