Polyhedral convex cones and the equational theory of the bicyclic semigroup
by
Francis J. Pastijn
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53201

With any balanced semigroup identity a number of polyhedral convex cones is associated. This provides us with a tool to formulate an algorithm to verify whether or not the given identity is satisfied in the bicyclic semigroup. This algorithm may even be presented in terms of the computation of a number of determinants. As a consequence, given any semigroup identity, it is decidable whether or not the variety determined by this identity contains simple semigroups which are not completely simple. A variant of this latter result is obtained : given any semigroup identity, it is decidable whether or not the variety determined by this identity contains an idempotent free simple semigroup.

Date received: November 19, 2001