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The Szendrei expansion of a semigroup

Part of: Semigroups

Published online by Cambridge University Press:  26 February 2010

John Fountain  and
Gracinda M. S. Gomes
John Fountain
Affiliation:
Department of Mathematics, University of York, Heslington, York, YO1 5DD
Gracinda M. S. Gomes
Affiliation:
Departamento de Matemàtica, Faculdade de Ciências, Universidade de Lisboa, 1700 Lisboa, Portugal.
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Extract

In the terminology of Birget and Rhodes [3], an expansion is a functor F from the category of semigroups into some special category of semigroups such that there is a natural transformation η from F to the identity functor for which ηs is surjective for every semigroup S. The three expansions introduced in [3] have proved to be of particular interest when applied to groups. In fact, as shown in [4], Ĝ(2) are isomorphic for any group G, is an E-unitary inverse monoid and the kernel of the homomorphism ηG is the minimum group congruence on . Furthermore, if G is the free group on A, then the “cut-down to generators” which is a subsemigroup of is the free inverse semigroup on A. Essentially the same result was given by Margolis and Pin [12].

MSC classification

Secondary: 20M50: Connections of semigroups with homological algebra and category theory
Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 251 - 260
Copyright
Copyright © University College London 1990

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References

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