A characterization of a ∼ admissible congruence on a weakly type B semigroup

In this article, the notions of ∼ \sim admissible congruences and ∼ \sim normal congruences on a weakly type B semigroup are characterized and the relationship between ∼ \sim admissible congruences and ∼ \sim normal congruences is investigated. In particular, some properties of such congruences on a weakly type B semigroup are given using an approach of kernel-trace. Finally, we extend the congruence pair on an inverse semigroup to the case of a weakly type B semigroup and obtain some results.