We introduce the notion of Weak idempotent ring (WIR, for short) which is arnring of characteristic 2 and a4 = a2 for each a in the ring. We obtain certainrnproperties of this class. Further we provide examples of weak idempotent ringsrnto have more deeper insight in studying the structure of weak idempotent rings.rnAn equivalent de_nition for a commutative WIR with unity is given. Also wernobtain certain characterization theorems in terms of completely prime ideals andrnleft completely primary ideals. We introduce the concept of one sided completelyrnprimary ideal and prove that a one sided completely primary ideal is completelyrnprime if the ideal contains all nilpotent elements of the ring. Also we prove thatrnevery local weak idempotent ring with unity is primary ring and the intersectionrnof all primary ideals of a commutative weak idempotent ring with unity is thernzero ideal. We construct a partial synthesis of weak idempotent rings and developrna subclass 2-Weak idempotent rings of the class of weak idempotent rings. Werninvestigate the structure of a weak idempotent ring with unity of 4 and 8 elements.rnFurther we prove that every proper ideal is nil whenever 0 and 1 are the onlyrnidempotent elements of the weak idempotent ring with unity. We characterize thernsemiprime and primary ideals of commutative weak idempotent rings with unityrnand prove that the class weak idempotent rings satis_es the K othe's conjecture.rnWe study the structure of submaximal ideals in a commutative weak idempotentrnring with unity and show that every submaximal ideal of a commutative weakrnidempotent ring with unity is either semiprime or primary. We prove that everyrnsubmaximal ideal of the product ring of two commutative WIRs with unity isrnsemiprime and the intersection of all submaximal ideals is the nilradical. Wernmake a study on the fraction of rings for commutative weak idempotent ringsrnwith unity. Finally, We obtain certain properties concerning submaximal idealsrnunder homomorphic images.