Regular Semigroup With Some Transversals

This dissertation consists of three chapters.We investigate regular semigroups with regular * transversals and its generalization.Chapter 1 is introduction and preliminaries.Chapter 2 is divided into three sections.The first section is preliminar-ies.The second section is devoted to the investigation of some properties of some types of regular *-transversals.Its properties are similar to the corresponding results on inverse transversals.For example,an regular "-transversal is multiplicative if and only if it is weakly multiplicative and quasi-ideal. In the three section, the natural partial order on a regular semigroup with a Q-regular "-transversal is characterized,and the conditions of the partial order on a regular semigroup with a Q-regular "-transversal to satisfy D-majorization(minor-ization)and ρ-majorization(minorization) are concluded.Chapter 3 is devoted to the generalization of a regular *- transversal.In this chapter a new concept of a weakly regular *- transversal in a regular semigroup is introduced.Some properties are given and a construction of a regular semigroup with a quasi-ideal weakly regular *- transversal is described.