Abundant Semigroups With Systems Of Subsemigroups

In this thesis, we study abundant semigroups having certain properties of subsemigroups. This thesis consists of two chapters.In chapter 1, we study unit abundant monoids. This notion is a natural stretch of u-IC quasi-adequate monoids. After obtaining some properties of this kind of semigroups, we establish the structure theorem for unit idempotent-connected abundant monoids.In chapter 2, we introduce the concept of associate *-unipotent *-subsemi groups. This notion is a natural generalization of associate inverse subsemigroups in the range of abudant semigroups. Some properties are obtained.