Certain Types Of E-inversive Semigroup And Congruence

In this thesis, some classes of E-inversive semigroups and some congruences are investigated.The first section is a brief introuduction. In the second section, some basic conceptions and preliminaries about E-inversive semigroups are introuduced and some properties of E-inversive semigroups are obtained. Two classes of new E-inversive semigroups, completely E-inversive semigroups and E-inversive E-center semigroups, are given. The relationships among completely E-inversive semigroups, E-inversive E-center semigroups and E-inversive E-semigroups are demonstrated by the following examples.In the third section, E-inversive E-semigroups are investigated. Some properties and equivalent terms of E-inversive E-semigroups are obtained. The equivalent conditions of E-inversive E-semigroups and E-dense semigroups are given, respectively.The fourth section is devoted to the characterizations of congruences on E-inversive semigroups. Firstly, some special congruences are obtained by a given congruence which satisfys condition (?), such as band congruences on E-inversive semigroups, semilattice congruences, band congruences, orthodox congruences on E-inversive E-semigroups, semilattice congruences, inverse congruences on E-dense semigroups and E-inversive E-center semigroups. Secondly, band congrueces on E-inversive E-semigroups and semilattice congruences on E-dense (E-inversive E-center) semigroups are characterized by a given Clifford congruence. Finally, inversecongruences on E-dense semigroups and Clifford congruences on E-inversive E-center semigroups are obtained, respectively.In the fifth section, some equivalent characterizations of special congruences on E-inversive semigroups are given. Define relations C, F, F0 byThe equivalent characterizations of some congruences are presented by relations C and F- idempotent-separating congruences, group congruences and semilattice congruences on E-dense semigroups, group congruences and band congruences on E-inversive E- semigroups. The equivalent characterizations of idempotent-separating congruences and group congruences on E-inversive E-semigroups satisfy condition (A) are obtianed by the relation F0, respectively.