Characterization of Weakly Primary Ideals over Non-commutative Rings

Abstract

In this paper, we introduce the concept of weakly primary ideals over non-commutative rings. Several results on weakly primary ideals over non-commutative rings are proved. We prove that a right (resp. left) weakly primary ideal P of a ring R that is not right (resp. left) primary satisfies P2= 0. We give useful characterization of weakly primary ideals over non-commutative rings with nonzero identities. We prove that every irreducible ideal of a right (resp. left) Noetherian ring R is right (resp. left) weakly primary ideal in R.