U-abundant semigroups with left central idempotents

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 M α ×Λ α , where M α is a unipotent monoid and Λ α 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.