Semi-abundant semigroups with quasi-Ehresmann transversals

Abstract

Chen (Communications in Algebra 27(2), 4275-4288, 1999) introduced and investigated orthodox transversals of regular semigroups.  In this paper, we initiate  the investigation of  quasi-Ehresmann transversals   of semi-abundant semigroups which are generalizations of orthodox transversals of regular semigroups. Some interesting properties associated with quasi-Ehresmann transversals are established. Moreover, a structure theorem of semi-abundant semigroups with quasi-ideal strong quasi-Ehresmann transversals is obtained. Our results generalize  and enrich  Chen's results.