The structure of bisimple left unipotent semigroups as ordered pairs

Abstract

Call a semigroup S left unipotent if eachℒ-class of S contains exactly one idempotent. A structure theorem for bisimple left unipotent semigroups is given which reduces to that of N. R. Reilly [8] for bisimple inverse semigroups. A structure theorem, alternative to one given by R. J. Warne [13], is given for the case when the band ES of idempotents of S is an ω-chain of right zero semigroups, and two applications of it are made.