共查询到20条相似文献,搜索用时 15 毫秒
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Norman R. Reilly 《Semigroup Forum》2012,84(1):176-199
In a manner similar to the construction of the fundamental group of a connected graph, this article introduces the construction
of a fundamental semigroup associated with a bipartite graph. This semigroup is a 0-direct union of idempotent generated completely
0-simple semigroups. The maximal nonzero subgroups are the corresponding fundamental groups of the connected components. Adding
labelled edges to the graph leads to a more general completely 0-simple semigroup. The basic properties of such semigroups
are examined and they are shown to have certain universal properties as illustrated by the fact that the free completely simple
semigroup on n generators and its idempotent generated subsemigroup appear as special cases. 相似文献
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We give necessary and sufficient conditions for various vertex-transitivity of Cayley graphs of the class of completely 0-simple semigroups and its several subclasses. Moreover, the question when the Cayley graphs of completely 0-simple semigroups are undirected is considered. 相似文献
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G. Mashevitzky 《Semigroup Forum》1997,54(1):83-91
A finite basis of pseudoidentities of the pseudovariety generated by all finite completely 0-simple semigroups is constructed.
Thus this pseudovariety is decidable.
Partially supported by Israel Ministry of Absorption 相似文献
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Eckehart Hotzel 《Journal of Pure and Applied Algebra》2002,170(1):35-66
We describe the semigroups S with 0 that are projective in the category of right S-objects, i.e. of centered right S-operands. Among them are the free semigroups with an adjoined zero, and several characterizations of this subclass are given. Two other classes, one of them close to free semigroups with 0, the other rather far apart, are discussed in detail. The first class consists of semigroups of finite and infinite sequences, with multiplication based on concatenation. The second is formed by the projectives in the category of (S,S)-biobjects. 相似文献
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Akihiro Yamamura 《Journal of Pure and Applied Algebra》2007,210(2):521-536
A variant of an HNN extension of an inverse semigroup introduced by Gilbert [N.D. Gilbert, HNN extensions of inverse semigroups and groupoids, J. Algebra 272 (2004) 27-45] is defined provided that associated subsemigroups are order ideals. We show this presentation still makes sense without the assumption on associated subsemigroups in the sense that it gives a semigroup deserving to be an HNN extension, and it is embedded into another variant using the automata theoretical technique based on combinatorial and geometrical properties of Schützenberger graphs. 相似文献
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Igor Dolinka 《Journal of Pure and Applied Algebra》2009,213(10):1979-1990
We show that a finite completely regular semigroup has a sub-log-exponential free spectrum if and only if it is locally orthodox and has nilpotent subgroups. As a corollary, it follows that the Seif Conjecture holds true for completely regular monoids. In the process, we derive solutions of word problems of free objects in a sequence of varieties of locally orthodox completely regular semigroups from solutions of word problems in relatively free bands. 相似文献
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Simon M. Goberstein 《Algebra Universalis》2005,53(4):407-432
A partial automorphism of a semigroup S is any isomorphism between its subsemigroups, and the set all partial automorphisms of S with respect to composition is an inverse monoid called the partial automorphism monoid of S. Two semigroups are said to be
if their partial automorphism monoids are isomorphic. A class
of semigroups is called
if it contains every semigroup
to some semigroup from
Although the class of all inverse semigroups is not
we prove that the class of inverse semigroups, in which no maximal isolated subgroup is a direct product of an involution-free periodic group and the two-element cyclic group, is
It follows that the class of all combinatorial inverse semigroups (those with no nontrivial subgroups) is
A semigroup is called
if it is isomorphic or antiisomorphic to any semigroup that is
to it. We show that combinatorial inverse semigroups which are either shortly connected [5] or quasi-archimedean [10] are
To Ralph McKenzieReceived April 15, 2004; accepted in final form October 7, 2004. 相似文献
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We prove that four different notions of Morita equivalence for inverse semigroups motivated by C∗-algebra theory, topos theory, semigroup theory and the theory of ordered groupoids are equivalent. We also show that the category of unitary actions of an inverse semigroup is monadic over the category of étale actions. Consequently, the category of unitary actions of an inverse semigroup is equivalent to the category of presheaves on its Cauchy completion. More generally, we prove that the same is true for the category of closed actions, which is used to define the Morita theory in semigroup theory, of any semigroup with right local units. 相似文献
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We obtain Schur–Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations. 相似文献
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M. Satyanarayana 《Semigroup Forum》1980,19(1):307-312
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In this paper,P-ordered andQ-ordered semigroups are studied. Some characterizations and properties of such semigroups are obtalned. Also the relationship between maximal (minimum) regular ordered semigroups and unitary regular semigroups is investigated.Research is partiallysupported by CUHK grant No. 220.600.080. 相似文献
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Valdis Laan 《Journal of Pure and Applied Algebra》2011,215(10):2538-2546
In this paper we study Morita contexts for semigroups. We prove a Rees matrix cover connection between strongly Morita equivalent semigroups and investigate how the existence of a unitary Morita semigroup over a given semigroup is related to the existence of a ‘good’ Rees matrix cover of this semigroup. 相似文献
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M.V. Lawson 《Journal of Pure and Applied Algebra》2011,215(4):455-470
We prove that two semigroups with local units are Morita equivalent if and only if they have a joint enlargement. This approach to Morita theory provides a natural framework for understanding McAlister’s theory of the local structure of regular semigroups. In particular, we prove that a semigroup with local units is Morita equivalent to an inverse semigroup precisely when it is a regular locally inverse semigroup. 相似文献
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In this paper, we characterize those numerical semigroups containing 〈n1,n2〉. From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators. 相似文献
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Let be a transformation semigroup of degree . To each element we associate a permutation group acting on the image of , and we find a natural generating set for this group. It turns out that the -class of is a disjoint union of certain sets, each having size equal to the size of . As a consequence, we show that two -classes containing elements with equal images have the same size, even if they do not belong to the same -class. By a certain duality process we associate to another permutation group on the image of , and prove analogous results for the -class of . Finally we prove that the Schützenberger group of the -class of is isomorphic to the intersection of and . The results of this paper can also be applied in new algorithms for investigating transformation semigroups, which will
be described in a forthcoming paper.
Received 16 December 1996; in final form 18 February 1997 相似文献
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K. Auinger 《Algebra Universalis》1995,34(2):185-190
It is shown that an existence varietyV of regular semigroups contains (all) free products if and only ifV consists solely of locally inverse orE-solid semigroups.Presented by B. M. Schein.The author is indebted to the Australian Research Council for financial support (ARC grant A69231516). 相似文献
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Let S be a multiplicative semigroup of matrices with nonnegative entries. Assume that the diagonal entries of the members of S form a finite set. This paper is concerned with the following question: Under what circumstances can we deduce that S itself is finite? 相似文献