Some Studies Of Good Congruences On The Generalized Inverse Semigroups

The congruence theory of semigroup is an important research field of semigroup theory.The congruences on the semigroup provide some information for the study of semigroup homomorphism,and some essential congruences of such semigroups serve as a basis for the establishment of the semigroup structure theorem.In the study of congruence theory of regular semigroups,kernel-trace method is one of the effective methods to study congruence on regular semigroups.On the basis of this method,good congruences on semiabundant semigroups are studied by using the generalized kernel trace method.In this paper,good congruences on a weakly ample semigroup and a Rees matrix semigroup over the semi-adequate semigroup T are mainly studied.Firstly,the concept of good congruence on weakly ample semigroup is introduced and for any normal congruence ? in the idempotent element set E(S)of S,the minimum good congruence and the maximum good congruences with the trace ? on S is obtained,and the properties of good congruence with the same trace on the weakly ample semigroup are given.Secondly,the maximum and the minimum good congruence of the weakly ample semigroup whose kernel is a normal subsemigroup are obtained.Thirdly,the concept of congruence pair on weakly ample semigroup S is introduced,and for any good congruence p on the weakly ample semigroup S,(tr?,ker?)is proved to be a congruence pair on S,thus the congruence related to(?,N)on S is obtained.Finally,The concept of Rees matrix semigroup over the semi-adequate semigroup T is given,and the properties of good congruences of Rees matrix semigroup over the semi-adequate semigroup T are studied.In addition,the good congruence of Rees matrix semigroups is characterized.