Abstract
AbstractA class of regular semigroups closed under taking direct products, regular subsemigroups and homomorphic images is ane(xistence)-variety of regular semigroups. The classof 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 objecton the setXinis 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. Henceis a homomorphic image of the absolutely free algebraof 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 ofin terms of sets and binary relations. As an application, a model of the free strict pseudosemilattice on a setXis obtained.
Publisher
Cambridge University Press (CUP)
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