The New Structure Theorem of Right-$e$ Wlpp Semigroups

Abstract

Wlpp semigroups are generalizations of lpp semigroups and regular semigroups. In this paper, we consider some kinds of wlpp semigroups, namely right-$e$ wlpp semigroups. It is proved that such a semigroup $S$, if and only if $S$ is the strong semilattice of $\mathcal{L}$-right cancellative planks; also if and only if $S$ is a spined product of a right-$e$ wlpp semigroup and a left normal band.