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U.W. Bangor - School of Informatics - Mathematics Preprints
1999
Semigroup and Automata Theory
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99.06 : KELLENDONK, J. & LAWSON, M.V.
Tiling Semigroups
Abstract:
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
Abstract:
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
Abstract:
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
Abstract:
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
Abstract:
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.
ftp:
gzipped postscript file,
james.ps.gz