Studies On E-inversive Semigroups

In this paper, we mainly study on E-inversive semigroups. Firstly, we in-vestigate the partial order on weak inverses of.E-inversive semigroups and some character. Secondly, we introduce the definition of a new kind of fuzzy equivalence relation on E-inversive semigroups and showed that it is a fuzzy congruences rela-tion on E-inversive semigroups. Thirdly, we introduce the definition of E-inversive E-semigroup with φ-kernel normal systems. It is described that the fuzzy regular congruences on the E-inversive E-semigroup with φ-kernel normal systems.