Characterization of Weakly Primary Ideals over Non-commutative Rings

Ashour, Arwa and Hamoda, Mohammad (2014) Characterization of Weakly Primary Ideals over Non-commutative Rings. International Mathematical Forum, 9 (34). pp. 1659-1667. ISSN 10.12988

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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 satis�es 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.

Item Type: Article
Uncontrolled Keywords: Prime ideal, primary ideal, weakly primary ideal, Jacobson radical, right weakly primary ideal, left weakly primary ideal
Subjects: Q Science > QA Mathematics
Depositing User: د. محمد العبد محمد حمودة
Date Deposited: 10 May 2018 07:09
Last Modified: 10 May 2018 07:09
URI: http://scholar.alaqsa.edu.ps/id/eprint/736

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