With Pure Cross-section Of Regular Semigroups,

This dissertation consists of five sections. We investigate regular semigroups with orthodox transversals. The first and second sections are introduction and preliminaries respectively. The third and forth sections are devoted to the investigation of the relationship between the quasi-ideal orthodox transversals of a regular semigroup and some properties of some types of orthodox transversals. The concept of orthodox transversal was first introduced in[13]. This is an interesting generalization of inverse transversal. As for inverse transversals, some important properties on regular semigroups with quasi-ideal inverse transversals were obtained[20,22,23]. As for orthodox transversal, the quasi-ideal orthodox transversals of a regular semigroup are not necessarily isomorphic, but the product of any two quasi-ideal orthodox transversals of a regular semigroup S is a quasi-ideal orthodox transversal of S is obtained in this dissertation. Thus the properties on orthodox transversals are different from the corresponding results on inverse transversals. A number of types of orthodox transversals are grouped together in section 4, its properties are similar to the corresponding results on inverse transversals. For example, an orthodox transversal is multiplicative if and only if it is weakly multiplicative and a quasi-ideal. E-orthodox transversal is special interesting. Let S be an E-orthodox transversal of a regular semigroup S. Then for any idempotent e in 5, the inverses of e in 5 are idempotents and S is weakly multiplicative; Let< E(S) >be the idempotent-generated regular subsemigroup of S. Then...