共查询到20条相似文献,搜索用时 15 毫秒
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本文考虑全正则子半群构成链的正则半群,得到了正则半群具有全正则子半群构成链的一个充分必要条件,这推广了Jones关于具有全正则子半群构成链的逆半群的结果.特别地,建立了具有全正则子半群构成链的完全0-单半群的结构. 相似文献
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Z. J. Tian 《Vestnik St. Petersburg University: Mathematics》2007,40(1):89-92
In this paper, we present necessary and sufficient conditions for the lattice of completely simple subsemigroups of a completely simple semigroup to be 0-modular or 0-semidistributive or join semidistributive. 相似文献
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A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups. 相似文献
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S.M. Maepa 《Quaestiones Mathematicae》2016,39(3):307-318
We study the character amenability of semigroup algebras. We work on general semigroups and certain semigroups such as inverse semigroups with a finite number of idempotents, inverse semigroups with uniformly locally finite idempotent set, Brandt and Rees semigroup and study the character amenability of the semigroup algebra l1(S) in relation to the structures of the semigroup S. In particular, we show that for any semigroup S, if ?1(S) is character amenable, then S is amenable and regular. We also show that the left character amenability of the semigroup algebra ?1(S) on a Brandt semigroup S over a group G with index set J is equivalent to the amenability of G and J being finite. Finally, we show that for a Rees semigroup S with a zero over the group G, the left character amenability of ?1(S) is equivalent to its amenability, this is in turn equivalent to G being amenable. 相似文献
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Every inverse semigroup possesses a natural partial order and therefore convexity with respect to this order is of interest.
We study the extent to which an inverse semigroup is determined by its lattice of convex inverse subsemigroups; that is, if
the lattices of two inverse semigroups are isomorphic, how are the semigroups related? We solve this problem completely for
semilattices and for inverse semigroups in general reduce it to the case where the lattice isomorphism induces an isomorphism
between the semilattices of idempotents of the semigroups. For many inverse semigroups, such as the monogenic ones, this case
is the only one that can occur. In Part II, a study of the reduced case enables us to prove that many inverse semigroups,
such as the free ones, are strictly determined by their lattices of convex inverse subsemigroups, and to show that the answer
obtained here for semilattices can be extended to a broad class of inverse semigroups, including all finite, aperiodic ones.
Received September 24, 2002; accepted in final form December 15, 2002. 相似文献
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Keith A. Kearnes 《Algebra Universalis》2001,46(3):373-387
We show that a locally finite variety is congruence join semidistributive if and only if it satisfies a congruence identity
that is strong enough to force join semidistributivity in any lattice.
Received February 9, 2000; accepted in final form November 23, 2000. 相似文献
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R. Gray 《Discrete Mathematics》2008,308(20):4801-4810
In this paper we are concerned with the following question: for a semigroup S, what is the largest size of a subsemigroup T?S where T has a given property? The semigroups S that we consider are the full transformation semigroups; all mappings from a finite set to itself under composition of mappings. The subsemigroups T that we consider are of one of the following types: left zero, right zero, completely simple, or inverse. Furthermore, we find the largest size of such subsemigroups U where the least rank of an element in U is specified. Numerous examples are given. 相似文献
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Let A2 be the variety generated by the five-element non-orthodox 0-simple
semigroup. This paper presents the identity bases for several subvarieties of
A2 that are not generated by any completely 0-simple or completely simple
semigroups. It will be shown that several subvarieties of A2, including the
variety generated by the five-element Brandt semigroup, are hereditarily finitely
based. 相似文献
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Peter R. Jones 《Semigroup Forum》2006,73(3):330-344
A lattice isomorphism between inverse semigroups S and T is an isomorphism between their lattices of inverse subsemigroups.
When S is combinatorial, it has long been known that a bijection is induced between S and T. Various authors have introduced
successively weaker "archimedean" hypotheses under which this bijection is necessarily an isomorphism, naturally inducing
the original lattice isomorphism. Since lattice-isomorphic groups need not have the same cardinality, extending these techniques
to the non-combinatorial case requires some means of tying the subgroups to the rest of the semigroup. Ershova showed that
if S has no nontrivial isolated subgroups (subgroups that form an entire D-class) then again a bijection exists between S
and T. Recently, this technique has been successfully exploited, by Goberstein for fundamental inverse semigroups and by
the author for completely semisimple inverse semigroups, under two different finiteness hypotheses. In this paper, we derive
further properties of Ershova's bijection(s) and formulate a "quasi-connected" hypothesis that enables us to derive both Goberstein's
and the author's earlier results as corollaries. 相似文献
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《数学学报(英文版)》2015,(7)
A semigroup is called completely J~((e))-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid.It is proved that completely J~((e))-simple semigroups form a quasivarr ity.Moreover,the construction of free completely J~((e))-simple semigroups is given.It is found that a free completely J~((e))-simple semigroup is just a free completely J~*-simple semigroup and also a full subsemigroup of some completely simple semigroups. 相似文献
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Alexei Vernitski 《Semigroup Forum》2009,78(3):486-497
We prove a number of results related to finite semigroups and their inverse subsemigroups, including the following. (1) A finite
semigroup is aperiodic if and only if it is a homomorphic image of a finite semigroup whose inverse subsemigroups are semilattices.
(2) A finite inverse semigroup can be represented by order-preserving mappings on a chain if and only if it is a semilattice.
Finally, we introduce the concept of pseudo-small quasivariety of finite semigroups, generalizing the concept of small variety. 相似文献
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M. Satyanarayana 《Semigroup Forum》1971,3(1):43-50
A multiplicative semigroup S with 0 is said to be a R-semigroup if S admits a ring structure. Isbell proved that if a finitely
generated commutative semigroup is a R-semigroup, then it should be finite. The non-commutative version of this theorem is
unsettled. This paper considers semigroups, not necessarily commutative, which are principally generated as a right ideal
by single elements and semigroups which are generated by two independent generators and describes their structure. We also
prove that if a cancellative 0-simple semigroup containing an identity is a R-semigroup, then it should be a group with zero.
Communicated by A. H. Clifford 相似文献