THE WORD PROBLEM FOR THE BIFREE COMBINATORIAL STRICT REGULAR SEMIGROUP

A class of regular semigroups closed under taking direct products, reg ular subsemigroups and homomorphic images is an e(xistence)-variety of regular semigroups. The class CJR of all combinatorial strict regular semigroups is the e-variety generated by the five element non-orthodo x completely 0-simple semigroup and consists of all regular subdirect products of combinatorial completely 0-simple semigroups and/or rectan gular bands. The bifree object BFCJR(X) on the set X in CJR is the nat ural concept of a 'free object' in the class CJR. BFCJR(X) is generate d by the set X and the set of formal inverses X' under the two binary operations of multiplication . and forming the sandwich element AND. H ence BFCJR(X) is a homomorphic image of the absolutely free algebra (F [2,2](X or X'), ., AND) of type [2,2] generated by X or X'. In this pa per we shall describe the associated congruence on F[2,2](X or X') and construct a model of BFCJR(X) in terms of sets and binary relations. As an application, a model of the free strict pseudosemilattice on a s et X is obtained.