共查询到18条相似文献,搜索用时 109 毫秒
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证明了H~#-富足半群S是正规密码H~#-富足半群当且仅当它是完全J~#-单半群的强半格.该结果也是正规密码超富足半群和正规密码群并半群分别在超富足半群和完全正则半群上的相应结构定理的推广. 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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证明了ο-超富足半群S是正规密码ο-超富足半群当且仅当它是完全Jο-单半群的强半格.该结果也是正规密码超富足半群和正规密码群并半群分别在超富足半群和完全正则半群上的相应结构定理的推广。 相似文献
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S为半群,如果S中的每个Lρ-类都含幂等元,称S为Lρ-富足半群.特别地,如果对任意的α∈S,集合Iα∩Lα^ρ都只含唯一的元素,称S为强Lρ-富足半群.在S上通过一个非恒等置换σ,给出了PI-强Lρ-富足半群的结构定理. 相似文献
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Orthodox semigroups whose idempotents satisfy a certain identity 总被引:2,自引:0,他引:2
Miyuki Yamada 《Semigroup Forum》1973,6(1):113-128
An orthodox semigroup S is called a left [right] inverse semigroup if the set of idempotents of S satisfies the identity xyx=xy
[xyx=yx]. Bisimple left [right] inverse semigroups have been studied by Venkatesan [6]. In this paper, we clarify the structure
of general left [right] inverse semigroups. Further, we also investigate the structure of orthodox semigroups whose idempotents
satisfy the identity xyxzx=xyzx. In particular, it is shown that the set of idempotents of an orthodox semigroup S satisfies
xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semigroup and a right inverse semigroup. 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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本文在正则半群上引入弱中间幂等元和拟中间幂等元,着重探讨了这两类幂等元的性质特征.构造了若干具有弱(拟)中间幂等元的正则半群,确定了弱中间幂等元和拟中间幂等元之间的关系,给出了弱中间幂等元和拟中间幂等元各自的等价判定,利用拟中间幂等元刻画了纯正半群.最后,得到了构造具有拟中间幂等元的正则半群的一般途径,并在此基础上进一步给出了判定正则半群是否具有乘逆断面的方法. 相似文献
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We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement also holds. We also prove that an ordered semigroup S is both regular and intra-regular if and only if every bi-ideal of S is an intra-regular (resp. semisimple) subsemigroup of S. An ordered semigroup S is both regular and intra-regular if and only if the left (resp. right) ideals of S are right (resp. left) quasi-regular subsemigroups of S. We characterize the chains of simple and regular semigroups, and we prove that S is a complete semilattice of simple and regular semigroups if and only if S is a semilattice of simple and regular semigroups. While a semigroup which is both π-regular and intra-regular is a semilattice of simple and regular semigroups, this does not hold in ordered semigroups, in general. 相似文献
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P-Ehresmann semigroups are introduced by Jones as a common generalization of Ehresmann semigroups and regular \(*\)-semigroups. Ehresmann semigroups and their semigroup algebras are investigated by many authors in literature. In particular, Stein shows that under some finiteness condition, the semigroup algebra of an Ehresmann semigroup with a left (or right) restriction condition is isomorphic to the category algebra of the corresponding Ehresmann category. In this paper, we generalize this result to P-Ehresmann semigroups. More precisely, we show that for a left (or right) P-restriction locally Ehresmann P-Ehresmann semigroup \(\mathbf{S}\), if its projection set is principally finite, then we can give an algebra isomorphism between the semigroup algebra of \(\mathbf{S}\) and the partial semigroup algebra of the associate partial semigroup of \(\mathbf{S}\). Some interpretations and necessary examples are also provided to show why the above isomorphism dose not work for more general P-Ehresmann semigroups. 相似文献
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Weakly left ample semigroups are a class of semigroups that are (2,1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α. It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In this paper we show that for every finite weakly left ample semigroup S, there is a finite proper weakly left ample semigroup ? and an onto morphism from ? to S which separates idempotents. In fact, ? is actually a (2,1)-subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A). 相似文献
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T. T. Bowman 《Semigroup Forum》1972,5(1):331-339
For a compact totally ordered space X, K. H. Hofmann and P. S. Mostert constructed a topological semigroup Irr (X)0 such that every compact irreducible semigroup with idempotents X is a surmorphic image of Irr (X)0 [2]. J. H. Carruth and M. Mislove pointed out that Irr (X)0 was in general not a compact semigroup. In this paper a compact connected hormos will be constructed which contains Irr (X)0 as a dense subsemigroup and for which every compact irreducible semigroup with idempotents X is a surmorphic image. This
leads to a new proof of the existence of generators for the category of compact irreducible semigroups with idempotents X.
It will then be shown that Irr (X)0 contains generators for the category. 相似文献
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Mohan S. Putcha 《Semigroup Forum》1971,3(1):51-57
In this paper we study commutative semigroups whose every homomorphic image in a group is a group. We find that for a commutative
semigroup S, this property is equivalent to S being a union of subsemigroups each of which either has a kernel or else is
isomorphic to one of a sequence T0, T1, T2, ... of explicitly given, countably infinite semigroups without idempotents. Moreover, if S is also finitely generated then
this property is equivalent to S having a kernel. 相似文献