Study On Congruence And Localization Of Some Semigroups

This thesis is mainly devoted to study the congruences and localization on somegeneralized regular semigroups The contents contain a special congruence on aneventually regular semigroup,the group congruences on E-inversive semigroups,theleast group congruences on E-dense semigroups and the localization of the Cliffordeventually regular semigroups'S semidirect product Details are as follows:Chapter l is the brief introduction of this paper,in which we show the researchbackgrounds,research ways and research contents of this thesisIn chapter 2．we are concerned with the characterization of a special congru-ence on an eventually regular semigroup First we defined a congruence∈on thesubsemigroup of eventually regular semigroup S,that is ,which generated byz(s),the set of all idempotent of S then the structure of the greatest rectangulargroup congruence with hyper-trace∈on S is givenIn chapter 3,we investigate the congruences on E-inversive semigroups Firstwe show that the joinγ∨Рo of the arbitrary group congruenceγand the arbitrary reg-ular congruence p on E-inversive semigroup S is also a group congruence on S Next,a representation and soiile characterizations of the least group congruence on theE-dense semigroups,namely,E-inversive semigroup with commuting idempotentsare given These results generalized soiile results on stronglyπ一inverse semigroupsand inverse semigroups,meanwhile,soiile new results on these semigroups are alsoobtainedChapter 4 discusses the localization of semidirect product of Clifford eventuallyregular semigroups,with respect to its semilattice of idempotents The result showsthat the localization of semidirect product S×ηT of two Clifford eventually regularsemigroups S and T at its semilattice of idempotents exists,which is isomorphicto the semidirect product of the localization of S at its semilattice of idempotentsz(s)and the localization of T at its semilattice of idempotents E(T)These resultsgeneralized the results on Clifford semigroups...