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Loganathan, M.; Tamilarasi, A.

Construction and representation of regular semigroups. (English) Zbl 0833.20077

Semigroup Forum 51, No. 2, 191-216 (1995).
This is a substantial paper which introduces a categorical framework for the study of various standard types of hulls of a regular semigroup. Familiarity with the notion of inductive groupoid and the theory of biordered sets is assumed. The method is based on the notion of a so called \(E\)-diagram in an arbitrary category \(C\) with respect to a regular biordered set \(E\). Specializations of \(C\) then allow the recovery of certain hull constructions. Explicit descriptions are given in the case where \(E(T)\) is the biordered set of idempotents of a semigroup \(T\) over a regular semigroup \(S\).
Reviewer: P.M.Higgins (Colchester)

Cited in 1 Review

MSC:

20M17 Regular semigroups
20M10 General structure theory for semigroups
20M50 Connections of semigroups with homological algebra and category theory
20M30 Representation of semigroups; actions of semigroups on sets

Keywords:

hulls of regular semigroups; inductive groupoids; biordered sets; \(E\)-diagrams; categories; regular biordered sets; hull constructions; idempotents; regular matrix semigroups
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Full Text: DOI EuDML Geodesic

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