Idempotent Separating Congruences in a Weak P-regular Semigroup

Abstract

Yamada and Sen introduced the concept of P-regularity[1] in a regular semigroup as a generalization of both the concept of "orthgodox" and the concept of "(special) involution". In [2] Sen and Chattopadhyay defined p-regular semigroup by weakening the defining conditions of P-regular semigroup. In this paper we call this p-regular semigroup as weak P-regular semigroup. In this paper firstly we give an alternate characterization of the maximum idempotent separating congruence and secondly we give a discription of the lattice of the idempotent separation congruences on a weak P-regular semigroup.