Some Remarks on Weakly Tripotent Rings

Abstract

In the mathematical literature there are three approaches to study a weakly tripotent ring. We provide a comparative study of these approaches and exhibit that a weakly tripotent ring defined as per one of these approaches is in harmony with a tripotent ring in various aspects as it is a commutative ring, a reduced ring and satisfies the identity $a^{5}=a$ for each $a \in R$ like tripotent rings however a weakly tripotent ring defined as per rest of two approaches fail to be in harmony with a tripotent ring with respect to these aspects.