Categories Wrpp Semigroups Features And Structures

This paper consists of three chapters. The aim of this paper is to study characterizations and constructions of two classes of wrpp semigroups. In the first chapter, we introduce some concepts, the background of this issue and some interesting known results. Then we tell readers what we will do in this paper. In the second chapter, firstly, strongly wrpp semigroups which satisfy permutation identities, is introduced. Then we obtain some properties for such semigroups, ample and essential condition on the set of all idempotents of such semigroup being rectangular band. By establishing a semilattice congruence p on S, it is shown that a strongly wrpp semigroup, which satisfies permutation identities, is a strong semilattice of the direct product of a commutative R-left cancellative monoids and a rectangular band. In the third chapter, firstly, we introduce the concept of a perfect wrpp semigroup. By investigating the relation between perfect wrpp semigroups and C-wrpp semigroups, we obtain some characterization theorems for such semigroups. In particular, the spined product structure of perfect wrpp semigroups is established, this is, a perfect wrpp semigroup is a spined product of a C-wrpp semigroup and a normal band. As an application of spined product structure, we prove that a perfect wrpp semigroup is a strong semilattice of the direct product of an R-left cancel lative monoids and a rectangular band.