U -ABUNDANT SEMIGROUPS WITH LEFT CENTRAL IDEMPOTENTS
Sun Yan, Xueming Ren, Gong Chunmei · 2015
In this paper, we study the semilattice decomposition of U-abundant semigroups with left central idempotents.By using this semilattice decomposition, it is proved that a semigroup S is a U-abundant semigroup with left central idempotents if and only if it is a strong semilattice of a direct product Mα×Λα, where Mα is a unipotent monoid and Λα is a right zero band.This result is the basis of the establishing of the structure theorem of U-abundant semigroups with left central idempotents.