U.W. Bangor - School of Informatics - Mathematics Preprints 1999
Semigroup and Automata Theory
98.25 : JAMES, H. & LAWSON, M.V.
An application of groupoids of fractions to inverse semigroups
Abstract:We describe an application of category theory to the theory of inverse semigroups:
we prove the P-theorem for E-unitary inverse semigroups using groupoids of fractions of their associated division categories.
Published in:Periodica Mathematica Hungarica 38 (1999) 43-54.
98.26 : KHAN, T.A. & LAWSON, M.V.
Variants of regular semigroups
Abstract:Let S be a semigroup, and let a \in S. Then a variant of S with respect to a is a semigroup with underlying set S and multiplication \circ defined by x \circ y = xay.
In this paper, we characterise the regularity preserving elements a such that (S,\circ) is also regular. Hickey showed that the set of regularity preserving elements can function as a replacement for the unit group when S does not have an identity. As an application, we characterise the regularity preserving elements in certain Rees matrix semigroups. We also establish connections with work of Loganathan and Chandrasekaran, and with McAlister's work on inverse transversals in locally inverse semigroups. We also investigate the structure of arbitrary variants of regular semigroups concentrating on how the local structure of a semigroup affects the structure of its variants.