J. Aust. Math. Soc.
81 (2006), 6396

Polyhedral convex cones and the equational theory of the bicyclic semigroup

F. Pastijn
Department of Mathematics, Statistics and Computer Science
Marquette University
Milwaukee WI 532011881
USA
francisp@mscs.mu.edu



Abstract

To any given balanced semigroup identity
a number of polyhedral convex cones are
associated. In this setting an algorithm is
proposed which determines whether the given
identity is satisfied in the bicylic semigroup


or in the semigroup


The semigroups
and
deserve our attention because a semigroup
variety contains a simple semigroup which is not
completely simple (respectively, which is
idempotent free) if and only if this variety
contains (respectively,
). Therefore, for a given identity
it is decidable whether or not the variety
determined by
contains a simple semigroup which is not
completely simple (respectively, which is
idempotent free).

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