Embedding theorems for proper inverse semigroups
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Theorem 1.3 as mentioned in this paper shows that any proper inverse semigroup P can be embedded in a semidirect product P of a semilattice and a group, where P is bisimple with identity.About:
This article is published in Journal of Algebra.The article was published on 1976-09-01 and is currently open access. It has received 46 citations till now. The article focuses on the topics: Inverse semigroup & Semigroup.read more
Citations
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The free ample monoid
TL;DR: It is shown that the free weakly E-ample monoid on a set X is a full submonoid of the free inverse monoid FIM(X) on X, and so coincides with both thefree weakly ample and the free ample monoid FAM(X).
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Inverse semigroups and extensions of groups by semilattices
Stuart W. Margolis,Jean-Eric Pin +1 more
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Proper weakly left ample semigroups
TL;DR: It is shown how the structure of semigroups in this class is based on constructing semig groups from unipotent monoids and semilattices, a class with properties echoing those of inverse semiggroups.
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The structure of pseudo-inverse semigroups
TL;DR: In this paper, it was shown that every pseudo-inverse semigroup divides a semidirect product of a completely simple semigroup and a semilattice, and that the structure theorem for pseudo-Inverse Semigroups can be expressed in terms of groups, semi-attices and morphisms.
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Semigroups whose idempotents form a subsemigroup
TL;DR: In this article, it was shown that every semigroup S in which the idempotents form a subsemigroup has an E-unitary cover with the same property.
References
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Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
Book
The theory of groups
TL;DR: The theory of normal subgroups and homomorphisms was introduced in this article, along with the theory of $p$-groups regular $p-groups and their relation to abelian groups.
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Groups, semilattices and inverse semigroups. II
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A Class of Irreducible matrix representations of an Arbitrary Inverse Semigroup
TL;DR: In this paper, it was shown that if S satisfies the minimal conditions on both principal left and right ideals, which together imply the minimal condition on principal two-sided ideals, the irreducible representations of S can ultimately be expressed explicitly in terms of group representations.