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