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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


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


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


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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