On weakly radical ideals of non-commutative rings

Abstract

For a commutative ring [Formula: see text] denote the Jacobson radical of the ring by [Formula: see text]. Khashan et al. introduced and studied J-ideals and weakly J-ideals for commutative rings with identity. In this paper, let [Formula: see text] be a non-commutative ring. We introduce weakly [Formula: see text]-ideals for a special radical [Formula: see text] and show that if [Formula: see text] is the Jacobson radical many of the results proved by Khashan et al. are also satisfied for non-commutative rings. The results for weakly J-ideals for non-commutative rings follow as special cases of a more general situation.