Polyhedral convex cones and the equational theory of the bicyclic semigroup
Francis J. Pastijn · Journal of the Australian Mathematical Society · 2006
Abstract To any given balanced semigroup identityU≈Wa 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 semigroupsBCandEdeserve 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 containsBC(respectively,E). Therefore, for a given identityU≈Wit is decidable whether or not the variety determined byU≈Wcontains a simple semigroup which is not completely simple (respectively, which is idempotent free).