Abstract
Relative to the operation of forming “basic products” the set of idempotents of a regular semigroup forms a partial binary algebra which has been axiomatically characterized by K.S.S. Nambooripad as a “biordered set” (K.S.S. Nambooripad, Structure of Regular Semigroups I, Memoirs, Amer. Math. Soc. 244 (1979)). In this paper we indicate some techniques for constructing biordered sets from semilattices and rectangular biordered sets. In particular we describe a construction of all coextensions of rectangular biordered sets by semilattices, a construction of solid biordered sets and a construction of all pseudo-semilattices. We show how all finite biordered sets may be constructed from (finite) semilattices and (finite) rectangular biordered sets.
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