Weakly U-abundant semigroups with strong Ehresmann transversals
Dandan Yang · Mathematica Slovaca · 2018
Abstract The class of weakly U-abundant semigroups is an important source of non-regular semigroups, and it is well studied by semigroup theorists in recent years. An important subclass, called Ehresmann monoids, is deeply investigated by Branco, Gomes and Gould in 2014. In this paper, we are concerned with weakly U-abundant semigroups with strong Ehresmann transversals. Our aim is to give a structure theorem for such semigroups following the standard “Rees Theorem” type approach. As a direct application of the main result, we reobtain the structure theorem of abundant semigroups with quasi ideal adequate transversals by Chen in 2000.