Congrences On Some Semigroups

In this dissertation, we describe congruences on some semigroup . The main ideal is to extend the concepts of kernel and trace. We give the concept of congruence pair ,adding up to some conditions . Finally ,we find out a bijection between congruence pairs and congruences.There are two chapters.In the first chapter, we deal with the LR-normal orthogroup congruence on regular semigroups.Firstly, we give the defintion of LR-normal orthogroup congruence pair (? K), composed of a normal subsemigroup K of S and a LR-normal band congruenceMoreover, we show that (htrp, kerp) is LR-normal orthogroup congruence pair of S and that p = P(htrp,kerp) for all Z-normal orthogroup congruence p on it. So we have this result that there is a bijection between the set of all LR-normal orthogroup congruence pair of S and set of all LR-normal orthogroup congruences of S.In the second chapter, we give the description of the r-semiprime rectangular group congruences on TT?orthodox .Firstly, we give the definition of r-semiprime rectangular group congruence pair (? K), composed of a normal subsemigroup K of S and a rectangular band congruence ?on E(S). K and satisfy the following conditions...