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IDEMPOTENT-SEPARATING EXTENSIONS OF REGULAR SEMIGROUPS (2004)
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@MISC{Tamilarasi04idempotent-separatingextensions,
author = {A. Tamilarasi},
title = {IDEMPOTENT-SEPARATING EXTENSIONS OF REGULAR SEMIGROUPS},
year = {2004}
}
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Abstract
ForaregularbiorderedsetE, the notion of E-diagram and the associated regular semigroup was introduced in our previous paper (1995). Given a regular biordered set E, an E-diagram in a category C is a collection of objects, indexed by the elements of E and morphisms of C satisfying certain compatibility conditions. With such an E-diagram A we associate a regular semigroup Reg E (A) havingE as its biordered set of idempotents. This regular semigroup is analogous to automorphism group of a group. This paper provides an application of Reg E (A) to the idempotent-separating extensions of regular semigroups. We introduced the concept of crossed pair and used it to describe all extensions of a regular semigroup S by a group E-diagram A. In this paper, the necessary and sufficient condition for the existence of an extension of S by A is provided. Also we study cohomology and obstruction theories and find a relationship with extension theory for regular semigroups. 1.
Keyphrases
idempotent-separating extension regular semigroups regular semigroups regular semigroup sufficient condition previous paper idempotent-separating extension certain compatibility condition biordered set associated regular semigroup extension theory group e-diagram obstruction theory regular semigroup reg crossed pair
