共查询到20条相似文献,搜索用时 109 毫秒
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Mario Petrich 《Semigroup Forum》2003,66(2):179-211
On any regular semigroup S, the least group congruence σ, the greatest idempotent pure congruence τ and the least band congruence β are used to give the M -classification of regular semigroups as follows. These congruences generate a sublattice Λ of the congruence lattice C(S) of S. We consider the triples (Λ, K, T), where K and T are the restrictions of the K- and T-relations on {C(S) to Λ. Such triples are characterized abstractly and form the objects of a category M whose morphisms are surjective T-preserving homomorphisms subject to a mild condition. The class of regular semigroups is made into a category M whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor from M to M. Several properties of the classification of regular semigroups induced by this functor are established. 相似文献
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Miyuki Yamada 《Semigroup Forum》1971,2(1):154-161
In the previous paper [6], it has been proved that a semigroup S is strictly regular if and only if S is isomorphic to a quasi-direct
product EX Λ of a band E and an inverse semigroup Λ. The main purpose of this paper is to present the following results and some relevant
matters:
(1) A quasi-direct product EX Λ of a band E and an inverse semigroup Λ is simple [bisimple] if and only if Λ is simple [bisimple], and (2) in case where
EX Λ has a zero element, EX Λ is O-simple [O-bisimple] if and only if Λ is O-simple [O-bisimple]. Any notation and terminology should be referred to
[1], [5] and [6], unless otherwise stated. 相似文献
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P-systems in regular semigroups 总被引:10,自引:0,他引:10
Miyuki Yamada 《Semigroup Forum》1982,24(1):173-187
In this paper, firstly it is shown that a regular semigroup S becomes a regular *-semigroup (in the sense of [1]) if and only
if S has a certain subset called a p-system. Secondly, all the normal *-bands are completely described in terms of rectangular
*-bands (square bands) and transitive systems of homomorphisms of rectangular *-bands. Further, it is shown that an orthodox
semigroup S becomes a regular *-semigroup if there is a p-system F of the band ES of idempotents of S such that F∋e, ES∋t, e≥t imply t∈F. By using this result, it is also shown that F is a p-system of a generalized inverse semigroup S if and
only if F is a p-system of FS.
Dedicated to Professor L. M. Gluskin on his 60th birthday 相似文献
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É. A. Golubov 《Mathematical Notes》1975,17(3):247-251
In this note it is proved that a regular semigroup whose subgroups are all finitely approximable is finitely approximable and that the set of idempotents of each principal factor is finite. As a corollary necessary and sufficient conditions are found for certain classes of regular semigroups to be finitely approximable.Translated from Matematicheskie Zametki, Vol. 17, No. 3, pp. 423–432, March, 1975.The author is grateful to L. N. Shevrin and Yu. N. Mukhin for their valuable observations and helpful discussions. 相似文献
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Peter R. Jones 《Semigroup Forum》2014,89(2):383-393
Yu, Wang, Wu and Ye call a semigroup \(S\) \(\tau \) -congruence-free, where \(\tau \) is an equivalence relation on \(S\) , if any congruence \(\rho \) on \(S\) is either disjoint from \(\tau \) or contains \(\tau \) . A congruence-free semigroup is then just an \(\omega \) -congruence-free semigroup, where \(\omega \) is the universal relation. They determined the completely regular semigroups that are \(\tau \) -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is \(\mathrel {\mathcal {J}}\) -congruence-free if and only if it is either a semilattice or has a single nontrivial \(\mathrel {\mathcal {J}}\) -class, \(J\) , say, and either \(J\) is a subsemigroup, in which case it is congruence-free, or otherwise its principal factor is congruence-free. Given the current knowledge of congruence-free regular semigroups, this result is probably best possible. When specialized to completely semisimple semigroups, however, a complete answer is obtained, one that specializes to that of Yu et al. A similar outcome is obtained for \(\mathrel {\mathcal {L}}\) and \(\mathrel {\mathcal {R}}\) . In the case of \(\mathrel {\mathcal {H}}\) , only the completely semisimple case is fully resolved, again specializing to those of Yu et al. 相似文献
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John Meakin 《Semigroup Forum》1970,1(1):232-235
The kernel of a congruence on a regular semigroup S may be characterized as a set of subsets of S which satisfy the Teissier-Vagner-Preston
conditions. A simple construction of the unique congruence associated with such a set is obtained. A more useful characterization
of the kernel of a congruence on an orthodox semigroup (a regular semigroup whose idempotents form a subsemigroup) is provided,
and the minimal group congruence on an orthodox semigroup is determined. 相似文献
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Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here, we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations. 相似文献
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R-unipotent congruences on regular semigroups 总被引:3,自引:0,他引:3
Gracinda M. S. Gomes 《Semigroup Forum》1985,31(1):265-280
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Let S be an eventually regular semigroup. The extensively P-partial congruence pairs and P-partial congruence pairs for S are defined. Furthermore, the relationships between the lattice of congruences on S, the lattice of P-partial kernel normal systems for S, the lattice of extensively P-partial kernel normal systems for S and the poset of P-partial congruence pairs for S are explored. 相似文献
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Semigroup Forum - This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their... 相似文献
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Orthodox congruences on regular semigroups 总被引:4,自引:0,他引:4
Gracinda M. S. Gomes 《Semigroup Forum》1988,37(1):149-166
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Matrices of bisimple regular semigroups 总被引:1,自引:0,他引:1
Janet E. Mills 《Semigroup Forum》1983,26(1):117-123
A semigroup S is a matrix of subsemigroups Siμ, i ε I, μ ε M if the Siμ form a partition of S and SiμSjν≤Siν for all i, j in I, μ, ν in M. If all the Siμ are bisimple regular semigroups, then S is a bisimple regular semigroup. Properties of S are considered when the Siμ are bisimple and regular; for example, if S is orthodox then each element of S has an inverse in every component Siμ. 相似文献
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