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U.W. Bangor - School of Informatics - Mathematics Preprints 1999

Semigroup and Automata Theory


Tiling Semigroups


It has recently been shown how to construct an inverse semigroup from any tiling: a construction having applications in K-theoretical gap-labelling. In this paper, we provide the categorical basis for this construction in terms of an appropriate group acting partially and without fixed points on an inverse category associated with the tiling.

Published in:

J Algebra 224 (2000) 140-150.

99.12 : LAWSON, M.V. & MARKI, L.

Enlargements and Coverings by Rees Matrix Semigroups


We formulate a general condition, called an enlargement, under which a semigroup T is covered by a Rees matrix semigroup over a subsemigroup.

Published in:

Monatsh. Math. 129 (2000) 191-195.

99.24 : SNELLMAN, J.

Factorisation in topological monoids


The aim of this paper is sketch a theory of divisibility and factorisation in topological monoids, where finite products are replaced by convergent products. The algebraic case can then be viewed as the special case of discretely topologised topological monoids.
In particular, we define the topological factorisation monoid, a generalisation of the factorisation monoid for algebraic monoids, and show that it is always topologically factorial: any element can be uniquely written as a convergent product of irreducible elements. We give some sufficient conditions for a topological monoid to be topologically factorial.

Published in:

99.25 : KHAN, T.A. & LAWSON, M.V.

Rees matrix covers for a class of semigroups with locally commuting idempotents


McAlister proved that every regular locally inverse semigroup can be covered by a regular Rees matrix semigroup over an inverse semigroup by means of a homomorphism which is locally an isomorphism. We generalise this result to the class of semigroups with local units whose local submonoids have commuting idempotents and possessing what we term a 'McAlister sandwich function'.

Published in:

Proc. Edin. Math. Soc. 44 (2001) 173-186.

99.29 : JAMES, H.

Applications of category theory to inverse semigroups


We investigate an application of category theory to the theory of inverse semigroups by generalising an existing proof of the P-theorem for E-unitary bisimple inverse monoids to a new proof of the P-theorem for arbitrary E-unitary inverse monoids. The main tools used in this thesis are the division category approach to describing inverse monoids and groupoids of fractions.

Published in:

U.W.Bangor Ph.D. thesis.

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