a1 Department of Mathematics, University of York, Heslington, York YO1 5DD
In this paper we will study the properties of a natural partial order which may bedefined on an arbitrary abundant semigroup: in the case of regular semigroups werecapture the order introduced by Nambooripad . For abelian PP rings our order coincides with a relation introduced by Sussman , Abian [1, 2] and further studied by Chacron . Burmistroviˇ  investigated Sussman's order on separative semigroups. In the abundant case his order coincides with ours: some order theoretic properties of such semigroups may be found in a paper by Burgess .
(Received February 19 1985)