Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - June 1987 - Volume 30, Issue 02  

Research Article

The natural partial order on an abundant semigroup

Mark V. Lawsona1

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 [24]. For abelian PP rings our order coincides with a relation introduced by Sussman [25], Abian [1, 2] and further studied by Chacron [7]. Burmistroviˇ [6] 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 [5].

(Received February 19 1985)