U.W. Bangor - School of Informatics - Mathematics Preprints 1997
Semigroup and Automata Theory
97.03 : LAWSON, M.V.
Abstract:This paper is the first in a sequence in which we investigate the algebraic structure of Kellendonk's one-dimensional tiling semigroups. However, as a prelude to studying the tiling semigroups themselves, we study here a class of inverse semigroups which are generated by disjoint elements which we call "McAlister semigroups". They were first introduced by Dom McAlister as a by-product of his work on inverse semigroups separated over a subsemigroup.
Published in:Journal of Algebra 202 (1998) 276-294.
97.27 : LAWSON, M.V.
The structure of 0-E-unitary inverse semigroups
I: the monoid case
Abstract:This is the first of three papers in which we generalise the classical McAlister structure theory for E-unitary inverse semigroups to those 0-E-unitary inverse semigroups which admit a 0-restricted, idempotent pure prehomomorphism to a primitive inverse semigroup.
In this paper, we concentrate on finding necessary and sufficient conditions for the existence of such prehomomorphisms in the case of 0-E-unitary inverse monoids.
A class of inverse monoids which satisfy our conditions are those which are unambiguopus except at 0, consequently our theory applies to the polycyclic monoids.