With Inverse Transversals Of Pure Semigroup

The research of regular semigroups with inverse transversals is one of the most important objects of algebraic semigroup theory.In this dissertation,two claases of orthodox semigroups with transversals are studied.The main results are as follows:1.The normal orthodox semigroups with inverse transversals were studied and one constructing method of this kind of semigroups was obtained.Further, we proved that every normal orthodox semigroup with inverse transversals is isomorphic to the quasi-direct product of a left normal band,an inverse semigroup and a right normal band.2.The regular orthodox semigroups with Clifford transversals were studied. By construting a left regular orthogroup congruence and a right regular orthogroup congruence on the regular orthodox semigroup with inverse tranversal, we obtained subdirect product decomposition of regular orthodox semigroups with Clifford transversals.We also proved that a regular orthodox semigroup with Clifford transversal is a regular orthogroup.