Some Studies On Abundant Semigroups

In this thesis, a special class of abundant semigroups are studied. The thesis is divided into three chapters.In chapter 1, we establish some characterizations of quasi-adequate semi-groups. It is proved that an abundant semigroup S is quasi-adequate if and only if for all a, b∈Reg(S), the product of a pre-inverse of a and a pre-inverse of b is a pre-inverse of ba. In addition, a characterization of naturally partial order of quasi-adequate semigroups is also obtained.In chapter 2, we define the naturally partial order≤e on an abun-dant semigroup. It is proved that for an abundant semigroup S, S is an idempotent-connected locally quasi-ad equate semigroup if and only if≤=≤e on S.In chapter 3, we define the RP-framed abundant semigroups. It is proved that a semigroup is a RP-framed abundant semigroup if and only if it is isomorphic to some Rees matrix semigroup M(T;i,A;P), where T is an abundant monoid and the entries of the matrix P lie in the group of units of T.