The word problem for the bifree combinatorial strict regular semigroup
Karl Auinger · Mathematical Proceedings of the Cambridge Philosophical Society · 1993
Abstract A class of regular semigroups closed under taking direct products, regular subsemigroups and homomorphic images is ane(xistence)-variety of regular semigroups. The class of all combinatorial strict regular semigroups is thee-variety generated by the five element non-orthodox completely 0-simple semigroup and consists of all regular subdirect products of combinatorial completely 0-simple semigroups and/or rectangular bands. The bifree object on the setXin is the natural concept of a ‘free object’ in the class . is generated by the setXand the set of formal inversesX′ under the two binary operations of multiplication · and forming the sandwich element ∧A. Hence is a homomorphic image of the absolutely free algebra of type 〈2, 2〉 generated by X ∪X′. In this paper we shall describe the associated congruence onF〈2, 2〉(X∪X′) and construct a model of in terms of sets and binary relations. As an application, a model of the free strict pseudosemilattice on a setXis obtained.