共查询到20条相似文献,搜索用时 15 毫秒
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João Araújo 《代数通讯》2013,41(10):3866-3878
We prove that given a finite (zero) exact right decomposition (M, T) of a semigroup S, if M is defined by a finite complete presentation, then S is also defined by a finite complete presentation. Exact right decompositions are natural generalizations to semigroups of coset decompositions in groups. As a consequence, we deduce that any Zappa–Szép extension of a monoid defined by a finite complete presentation, by a finite monoid, is also defined by such a presentation. It is also proved that a semigroup M 0[A; I, J; P], where A and P satisfy some very general conditions, is also defined by a finite complete presentation. 相似文献
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The purpose of this paper is twofold. First we determine some forms of the relations in a finite semigroup presentation with
zero deficiency which does or does not define a group. Moreover, we conclude that a finite Rees matrix semigroup M
[G; I, Λ; P] is efficient when G is efficient and the index sets I, Λ are finite. 相似文献
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A semigroup is complex if it generates a variety the subvariety lattice of which contains an isomorphic copy of every finite
lattice. It is known that a complex semigroup has at least four elements and that up to isomorphism and anti-isomorphism,
there are four complex semigroups of order four. Subvarieties of the varieties generated by two of these four minimal complex
semigroups have previously been described. To complete the study, we describe subvarieties of the varieties generated by the
remaining two semigroups.
This research was partially supported by the National Natural Science Foundation of China (No.10571077) and the Natural Science
Foundation of Gansu Province (No.3ZS052-A25-017) 相似文献
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Let G/H be an irreducible globally hyperbolic semisimple symmetric space, and let S ³ G be a subsemigroup containing H not isolated in S . We show that if So p 0 then there are H -invariant minimal and maximal cones C min ³ C max in the tangent space at the origin such that H exp C min ³ S ³ HZK (a)expC max . A double coset decomposition of the group G in terms of Cartan subspaces and the group H is proved. We also discuss the case where G/H is of Cayley type. 相似文献
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On Minimal and Maximal Left Ideals in Ordered Semigroups* 总被引:4,自引:0,他引:4
The concept of maximal left ideals is introduced in ordered semigroups. Characterizatations of minimal left and maximal left ideals are given. 相似文献
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《数学的实践与认识》2019,(21)
重新研究为解决Shevrin一个公开问题所用到的两个由表示定义的半群,给出其乘法表,利用数学软件GAP构造与之同构的变换半群,从而说明其中任一半群所含诸元素的互异;同时,还利用GAP对两个半群的结构性质进行验证.是对作者解决问题所发表文献的有益补充. 相似文献
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?evik 《Semigroup Forum》2008,66(1):1-17
Abstract. In recent papers of Ruskuc, Saito and J. Wang, the semi-direct product of two arbitrary monoids and a standard presentation,
say P, for this product have received considerable attention. Wang defined a trivialiser set of the Squier complex associated with
P and after that necessary and sufficient conditions for P to be efficient have been given by Cevik. As a main result of this paper, we give sufficient conditions for a presentation
of the semi-direct product of a one-relator monoid by an infinite cyclic monoid to be minimal but not efficient . In the final part of this paper we give some applications of this result. 相似文献
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We study disjointness classes of extensions of minimal topological transformation semigroups. 相似文献
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《代数通讯》2013,41(12):4713-4731
Abstract Let S be a numerical semigroup and let I be a relative ideal of S. Let S ? I denote the dual of I and let μ S (?) represent the size of a minimal generating set. We investigate the inequality μ S (I)μ S (S ? I) ≥ μ S (I + (S ? I)) under the assumption that S has multiplicity 8. We will show that if I is non-principal, then the strict inequality μ S (I)μ S (S ? I) > μ S (I + (S ? I)) always holds. 相似文献
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Generalized Bicyclic Semigroups and Jones Semigroups 总被引:1,自引:0,他引:1
In this paper, we consider the generalized bicyclic semigroups Bn = a, b | anb = 1 and the Jones semigroups An = a, b | an+1b = a. They are the generalizations of the bicyclic semigroup B = a, b | ab = 1 and its analogous semigroup A = a, b | a2b = a discovered by P.R., Jones in 1987. The word problem for these kinds of semigroups is solved. It is proved that, for n 2, Bn are bisimple right inverse but not inverse semigroups and that the semigroup C = a, b | a2b = a, ab2 = b is the smallest idempotent-free homomorphic image of An. Moreover, we also prove that An and Am are mutually embeddable but not isomorphic with each other if n m. As a consequence, different kind of
-nontrivial [0-]simple semigroups without idempotents are discussed.AMS 1991 Subject Classification: primary 20M10 secondary 20M05.Supported by NNSF of China (19671063) and KSRF of Sichuan Education Committee ([1999]127). 相似文献
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广义双循环半群和Jones半群 总被引:4,自引:0,他引:4
本文刻画了广义双循环半群Bn=〈a,b|a^nb=1〉和Jones半群An=〈a,b|a^n+1b=a〉(n≥1)的结构;证明了每个An都具有P.R.Jones所发现的半群A=〈a,b|a^2b=a〉的所有重要性质,特别地,证明了An,Am可互相嵌入,从而得到:第三个D-非平凡的无幂等元「0-」单半群若不含C=〈a,b|a^2b=a,abT^2=b〉,则必含每个An或它们的对偶,作为推论,每人广义 相似文献
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A. Sinan Çevik 《代数通讯》2013,41(8):2583-2587
Let R be a ring and M(R) the set consisting of zero and primitive idempotents of R. We study the rings R for which M(R) is multiplicative. It is proved that if R has a complete finite set of primitive orthogonal idempotents, then R is a finite direct product of connected rings precisely when M(R) is multiplicative. We prove that if R is a (von Neumann) regular ring with M(R) multiplicative, then every primitive idempotent in R is central. It is also shown that this does not happen even in semihereditary and semiregular rings. Let R be an arbitrary ring with M(R) multiplicative and e ∈ R be a primitive idempotent, then for every unit u ∈ R, it is proved that eue is a unit in eRe. We also prove that if M(R) is multiplicative, then two primitive idempotents e and f in R are conjugates, i.e., f = ueu ?1 for some u ∈ U(R), if and only if ef ≠ 0. 相似文献
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A module M is said to be extending (𝒢-extending) if for each submodule X of M there exists a direct summand D of M such that X is essential in D (X ∩ D is essential in both X and D). It is known that for a nonsingular module the concepts of 𝒢-extending and extending coincide. However, in the not nonsingular case, they are distinct. In this article, we obtain a characterization of the right 𝒢-extending generalized triangular matrix rings. This result and its corollaries improve and generalize the existing results on right extending generalized triangular matrix rings. It is well known that the ring of n-by-n triangular matrices over a right selfinjective ring is not, in general, right extending. One application of our characterization shows that such rings are right 𝒢-extending. Connections to Operator Theory and a characterization of the class of right extending right SI-rings are also obtained. Examples are given to illustrate and delimit the theory. 相似文献
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Research supported by NSERC. 相似文献
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Let S =∪(Gα : α∈ E) be a semilattice of groups(i.e., a Cliford semigroup) and n a natural number. E is called an n-element chain of groups if it is an n-element chain. Denote by Cn the set of all n-element chains of groups. In this paper we shall show that for any natural number n, the class of semigroups Cn satisfies the strong isomorphism property. 相似文献
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Let S =∪(Gα : α ∈ E) be a semilattice of groups(i.e., a Cliford semigroup) and n a natural number. E is called an n-element chain of groups if it is an n-element chain. Denote by Cn the set of all n-element chains of groups. In this paper we shall show that for any natural number n, the class of semigroups Cn satisfies the strong isomorphism property. 相似文献
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