Congruences on ωn-Bisimple Semigroups
R. J. Warne · Journal of the Australian Mathematical Society · 1969
LetSbe a bisimple semigroup and letEsdenote its set of idempotents. We may partially orderEsin the following manner: ife,f∈Es,e≧fif and only ifef=fe=e. We then say thatEsis under or assumes its natural order. LetI0denote the non-negative integers and letndenote a natural number. IfEs, under its natural order, isomorphic to (I0)nunder the reverse of the usual lexicographic order, we callSan ωn-bisimple semigroup. (See [9] for an explanation of notation.) We determined the structure of ωn-bisimple semigroups completely mod groups in [9]. The ωn-bisimple semigroups, theI-bisimple semigroups [8], and the ωnI-bisimple semigroups [9] are classes of simple semigroups except completely simple semigroups whose structure has been determined mod groups.