Bulletin of the Australian Mathematical Society

Table of Contents - 1993 - Volume 48, Issue 01  

Research Article

On semigroups with involution

D. Easdowna1 and W.D. Munna2

a1 School of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, Australia

a2 Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland United Kingdom

A semigroup S with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S,

S0004972700015495_eqnU1

.

It is shown that a semigroup is inverse if and only if it is a special involution semigroup in which every element invariant under the involution is periodic. Other examples of special involution semigroups are discussed; these include free semigroups, totally ordered cancellative commutative semigroups and certain semigroups of matrices. Some properties of the semigroup algebras of special involution semigroups are also derived. In particular, it is shown that their real and complex semigroup algebras are semiprimitive.

(Received August 19 1992)