Abstract: On the base of the construction of abundant semigroups with a normal mallal idempotent[14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent.Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtainedby Blyth and McFadden^[3].

Key words: abundant semigroups, natural order, greatest idempotents