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U.W. Bangor - School of Informatics - Mathematics Preprints 1994

Semigroup and Automata Theory


94.12 : LAWSON, M.V.

Enlargements of regular semigroups

Abstract:

We introduce a clas of regular extensions of regular semigroups, called enlargements; a regular semigroup T is said to be an enlargement of a regular subsemigroup S if S = STS and T = TST. We show that S and T have many properties in common, and that enlargements may be used to analyse a number of questions in regular semigroup theory.

Published in:

Proc Edin Math Soc, 39 (1996) 425-460.


94.13 : LAWSON, M.V.

A class of actions of inverse semigroups

Abstract:

We generalise the clasical Munn representation of an inverse semigroup with the introduction of what we call ordered representations of inverse semigroups. Both the Wagner-Preston Representation and the effective actions of O'Carroll and McAlister are examples of such representations. We show that every ordered representation of an inverse semigroup S determines and is determined by a special kind of cover of S. As applications, we provide a fully categorical account of the theory of idempotent pure congruences, and we show that every inverse semigroup which is a semilattice with respect to the natural partial ordering is an image of a combinatorial inverse semigroup under an L-bijective, prehomomorphism.

Published in:

Journal of Algebra, 179, 1996, 570-598.


94.15 : LAWSON, M.V.

Rees matrix semigroups over semigroupoids and the structure of a class of abundant semigroups

Abstract:

McAlister proved that every locally inverse regular semigroup is a locally isomorphic image of a regular Rees matrix semigroup over an inverse semigroup. In this paper, we show how this result can be generalised to a class of locally adequate abundant semigroups.

Published in:

Acta Scientiarum Mathematicarum (Szeged) 66 (2000) 517-540.


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