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Representation of inverse monoids by partial automorphisms

Citation

FitzGerald, DG, Representation of inverse monoids by partial automorphisms, Semigroup Forum, 61, (3) pp. 357-362. ISSN 0037-1912 (2000) [Refereed Article]

DOI: doi:10.1007/PL00006034

Abstract

It is shown that any inverse semigroup of endomorphisms of an object in a properly (E, M)-structured category admitting intersections may be embedded in an inverse monoid of partial automorphisms between retracts of that object. It follows that every inverse monoid is isomorphic with an inverse monoid of all partial automorphisms between [non-trivial] retracts of some object of any [almost] algebraically universal and properly (E, M)-structured category with intersections; in particular, of an [almost] algebraically universal and finitely complete category with arbitrary intersections. Several examples are given.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Group Theory and Generalisations
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:FitzGerald, DG (Dr Des FitzGerald)
ID Code:18677
Year Published:2000
Deposited By:Mathematics
Deposited On:2000-08-01
Last Modified:2011-08-04
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