Primary Submaximal Ideals in Commutative Weak Idempotent Rings

Abstract

Let R be a commutative weak idempotent ring (cWIR, for short) with unity, N and  be the set of all nilpotent and idempotent elements of R respectively. In this paper, we study the structure of primary submaximal ideals in R and prove that, if P is a primary submaximal ideal of R and   for some   , then  is a maximal ideal of R and  , where .