共查询到17条相似文献,搜索用时 125 毫秒
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本文引入了--格林关系和--富足半群,研究了满足同余条件含有中间幂等元的--富足半群.利用具有中间幂等元的由幂等元生成的正则半群和◇-拟恰当半群建立了满足同余条件含有中间幂等元的◇-富足半群的结构. 相似文献
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具有正规中间幂等元的富足半群的构造 总被引:1,自引:0,他引:1
本文研究富足半群上中间幂等元的若干性质,并给出了具有正规中间幂等元的富半群的构造。作为推论,我们得到Blyth和McFadden[1]及E1-Qallali[2]中相应结果。 相似文献
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具有弱正规幂等元的富足半群的结构 总被引:7,自引:1,他引:6
本文研究含弱正规幂等元的富足半群.在给出这类半群的若干特征后,建立了具有弱正规幂等元的富足半群的结构.作为应用,给出具有正规幂等元的富足半群和具有(弱)正规幂等元的拟适当半群的结构. 相似文献
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陈露 《纯粹数学与应用数学》2011,27(4):433-436
为了深入研究N(2,2,0)代数的代数结构,在N(2,2,0)代数中建立了中间幂等元的概念,讨论了它的基本性质,给出了中间幂等元关联的集合坞是(S,*,△,0)的子代数的一个条件.证明了当U(2,2,0)代数中包含一个右零半群时,Mg是幂等元集E(S)的子集.并利用坞定义了一个等价关系. 相似文献
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本文研究了一类特殊的左富足半群,即左GC-lpp-半群上的R*-同余.我们利用类似正则半群上同余的核迹方法分别刻画了这类半群上具有相同核和迹的最大和最小同余.同时,我们也得到了左GC-lpp-半群上的幂等元R*-同余的一些性质,并建立了这种同余的结构. 相似文献
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An ordered pair (e, f) of idempotents of a regular semigroup is called a skew pair
if ef is not idempotent whereas fe is idempotent. We have shown previously
that there are four distinct types of skew pairs of idempotents. Here we
consider the smallest regular semigroups that contain precisely one of each of
these four types. We show that, to within isomorphism and dualisomorphism,
there are six such semigroups and characterise them as quotient semigroups of
certain regular Rees matrix semigroups. 相似文献
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A semigroup is regular if it contains at least one idempotent in each ?-class and in each ?-class. A regular semigroup is inverse if it satisfies either of the following equivalent conditions: (i) there is a unique idempotent in each ?-class and in each ?-class, or (ii) the idempotents commute. Analogously, a semigroup is abundant if it contains at least one idempotent in each ?*-class and in each ?*-class. An abundant semigroup is adequate if its idempotents commute. In adequate semigroups, there is a unique idempotent in each ?* and ?*-class. M. Kambites raised the question of the converse: in a finite abundant semigroup such that there is a unique idempotent in each ?* and ?*-class, must the idempotents commute? In this note, we provide a negative answer to this question. 相似文献
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In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related
to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979,
as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts
with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup,
and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the
fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from
regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that
an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the
*-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some
conclusions about the lattice of congruences of a *-regular semigroup.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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An ordered pair (e,f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent.
Previously [1] we have established that there are four distinct types of skew pairs of idempotents. We have also described
(as quotient semigroups of certain regular Rees matrix semigroups [2]) the structure of the smallest regular semigroups that
contain precisely one skew pair of each of the four types, there being to within isomorphism ten such semigroups. These we
call the derived Rees matrix semigroups. In the particular case of full transformation semigroups we proved in [3] that TX contains all four skew pairs of idempotents if and only if |X| ≥ 6. Here we prove that TX contains all ten derived Rees matrix semigroups if and only if |X| ≥ 7. 相似文献
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Olga Sapir 《Semigroup Forum》2005,71(1):140-146
For every semigroup of finite exponent whose chains of idempotents are
uniformly bounded we construct an identity which holds on this semigroup but
does not hold on the variety of all idempotent semigroups. This shows that the
variety of all idempotent semigroups E is not contained in any finitely generated
variety of semigroups. Since E is locally finite and each proper subvariety of E is
finitely generated [1, 3, 4], the variety of all idempotent semigroups is a minimal
example of an inherently non-finitely generated variety. 相似文献
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T. S. BLYTH M. H. ALMEIDA SANTOS 《数学学报(英文版)》2006,22(6):1705-1714
An ordered pair (e, f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent. We have shown previously that there are four distinct types of skew pairs of idempotents. Here we investigate the ubiquity of such skew pairs in full transformation semigroups. 相似文献
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A subgroup H of a regular semigroup S is said to be an associate subgroup of S if for every s ∈ S, there is a unique associate of s in H. An idempotent z of S is said to be medial if czc = c, for every c product of idempotents of S. Blyth and Martins established a structure theorem for semigroups with an associate subgroup whose identity is a medial idempotent, in terms of an idempotent generated semigroup, a group and a single homomorphism. Here, we construct a system of axioms which characterize these semigroups in terms of a unary operation satisfying those axioms. As a generalization of this class of semigroups, we characterize regular semigroups S having a subgroup which is a transversal of a congruence on S. 相似文献