@Article{CMR-33-2, author = {Liu, Jingguo and Zhang, Jinling}, title = {$\cal P$-Congruence-Free Epigroups}, journal = {Communications in Mathematical Research }, year = {2017}, volume = {33}, number = {2}, pages = {97--109}, abstract = {
Let $\cal P$ denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any congruence either contains $\cal P$ or its join with $\mathcal P$ is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.