Two Classes Of Lpp Semigroups Of Type F

In this thesis, two classes of left pp semigroups of type F are studied. This thesis is divided into two chapters and consists of two integrated papers.In Chapter 1, we introduce the concept of pre-homomorphism and characterize F-abundant semigroups in terms of it.It presents the structure of F-abundant semigroups in another way.In Chapter 2, a left GC — lpp semigroup of type F is defined as a left GC — lpp semigroup which is an F-lpp semigroup. We introduce FGC-systems and MFG-McAlister admissible triples, and furthermore establish the structures of left GC — lpp monoids of type F in terms of FGC-systems and MFG-McAlister admissible triples, respectively. In particular, it is verified that any left GC — lpp semigroup of type F in which the minimal right cancellative monoid congruence is a cancellative congruence can be embedded into a semidirect product of a left regular band by a cancellative monoid. In addition, some special cases are considered.