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 .