VARIETIES GENERATED BY COMPLETELY 0-SIMPLE SEMIGROUPS
نویسندگان
چکیده
منابع مشابه
Limit Varieties Generated by Completely 0-Simple Semigroups
A variety of semigroups that is minimal with respect to being non-finitely based is said to be a limit variety. By Zorn’s Lemma, each non-finitely based variety contains at least one limit subvariety. Although many examples of non-finitely based varieties are known in the literature (see [3, 5]), explicit examples of limit varieties are very rarely discovered [1, 2, 4]. The objective of the pre...
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A formula for the rank of an arbitrary finite completely 0-simple semigroup, represented as a Rees matrix semigroup M[G; I,Λ;P ] , is given. The result generalises that of Ruškuc concerning the rank of connected finite completely 0-simple semigroups. The rank is expressed in terms of |I| , |Λ| , the number of connected components k of P and a number rmin which we define. We go on to show that t...
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In this paper completely simple semigroups or generalized groups are considered. We characterize generalized groups which are normal generalized groups. Homomorphisms of generalized groups are considered. Equivalent conditions for the kernel of a homomorphism are deduced. We prove that the group components of a generalized group have the same cardinality. We also prove that if G is a finite nor...
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Completely regular semigroups CR are regarded here as algebras with multiplication and the unary operation of inversion. Their lattice of varieties is denoted by L.CR/. Let B denote the variety of bands and L.B/ the lattice of its subvarieties. The mapping V → V ∩ B is a complete homomorphism of L.CR/ onto L.B/. The congruence induced by it has classes that are intervals, say VB = [VB ;V B] for...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2008
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788708000311