On Abundant Semigroups with Weak Normal Idempotents

Abstract

Weak normal idempotent of abundant semigroup was introduced by Guo[7]. In this paper, weak normal idempotents and normal idempotents of abundant semigroups are respectively characterized in many different ways. These results enable us to obtain an non-regular abundant semigroup which contains a non-normal weak normal idempotent. The example shows that weak normal idempotent make sense and lead us to deduce that the main result of [2] can not be generalized into the class of abundant semigroups. At last, we investigate some conditions under which every weak normal idempotent must be normal.