In this paper, the concepts of Soft E-inversive semigroup, soft normal semigroup on E-inversive semigroup will be defined. Some results will be obtained. Finally, the concept of soft group congruence on Soft E-inversive semigroup is given, and the connections among soft group congruence and soft normal semigroup on E-inversive semigroup are revealed.

Abstract:In this paper, the concepts of soft inverse semigroup, soft normal semigroup on inverse semigroup, and soft morphism are given. Some characterizations and results are obtained. Next, the definitions of soft group congruence on inverse semigroup is introduced, the relationship between soft group congruence and soft normal semigroup on inverse semigroup are studied more.