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Abstract
The purpose of this dissertation is to characterize the structure of certain classes of regular semigroups. A semigroup possessing no congruences other that the identity congruence and the universal congruence is called congruence-free. This class of regular semigroups gives insight into the study of any semigroup, since it has been shown by Sutov and by Munn that any semigroup can be imbedded in congruence-free a semigroup. The problem of determining the structure
of congruence-free semigroups has been considered by Gluskin [5] on semigroups with zero, by Munn on
inverse semigroups and recently by Baird on inverse semigoups with zero. In Chapter I we obtain an answer to this problem for certain classes of semigroups and extend some of the results of Munn.
