A Bundant Semigroups

In this thesis abundant semigroup are studied. This thesis consists of two chapters.In chapter 1, congruences on semigroups are always main subjects of semigroup theory. It must be faced in the course of studying good congruences whether joins of good congruences are good. We give a negative answer to this problem. It is well known that congruences on regular semigroups are good. Therefore, joins of good congruence on a regular semigroup is a good one. The problem is naturally given whether there exist an irregular semigroup in which joins of good congruences are good. We give a positive solution.In chapter 2, we prove that an abundant semigroup satisfying the regularity is a locally E-solid [resp. quasi-adequate; R*- unipotent] semigroup if and only if it is an E-local isomorphic image of some abundant Rees matrix semigroup AM(T; I, A; P) over an E-solid abundant [resp. quasi-adequate; R*- unipotent] semigroup with entries of the sandwich matrix P being regular elements of T. These extend the results in McAlister[21].