Some Studies Of Locally Adequate Semigroups

In this thesis, some subclasses of locally adequate semigroups are studied. This thesis consists of two Chapters.In Chapter 1, we first study the properties of a natural partial order which may be denned on an arbitrary abundant semigroup. In the case of regular semigroups we recapture the order introduced by Nambooripad [ 16 ]. In fact, many properties and constructions on abundant semigroups may be described in terms of its natural partial order. In Section 2, We prove that an IC-abundant semigroup is locally type A if and only if the natural partial order on the semigroup is compatible with the multiplication.In Chapter 2, we will study good congruences on perfect rectangular bands of adequate semigroups. After obtaining some characterizations of good congruences on such semigroups, we establish the structure of good congruences on perfect rectangular bands of adequate semigroups. In addition, we prove that the homomorphic images of perfect rectangular bands of adequate semigroups are perfect rectangular bands of adequate semigroups.