The structure of bisimple left unipotent semigroups as ordered pairs

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 E_S of idempotents of S is an ω-chain of right zero semigroups, and two applications of it are made. This research was partially supported by a grant from the National Science Foundation.