Abstract
In his fundamental paper, “On the structure of semigroups” [6], J. A. Green has examined certain important minimal conditions which may be satisfied bya semigroup S.We say that S satisfies the minimal condition on principal left ideals if every set of principal left ideals of S contains a minimal member with respect to inclusion:this condition is denoted by ℳ1. The corresponding conditions on principal rightideals and principal two-sided ideals are denoted by ℳr and ℳ1 respectively. The purpose of the present paper is to give some further results concerning these three conditions.Extensive use is made of the work of A. H. Clifford ([3] and [4]) onminimal ideals.
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