Some Results on AWN-injective Rings

Mar 1, 2024

Journal NTU Journal of Pure Sceinces

publisher hazem tallat

DOI https://doi.org/10.56286/ntujps.v3i4

Issue 2789-1089

A concept of AWN-injective ring is defined by [1], that is, for any 𝑎∈𝑁𝐷,there exists 𝑛≥1and an Y-submodule𝑋𝑎of 𝜇(𝜇is aright 𝐷-module) such that 𝑎𝑛≠0and 𝑙𝜇𝑟𝑅𝑎𝑛=𝜇𝑎𝑛⊕𝑋𝑎𝑛as left S-modulewith S=End(𝜇). If 𝐷𝐷is AWN-injective module, then we call 𝐷aright AWN-injective ring. In this note also continue to study some extensions of AWN-injective rings. A mong others it is proved that, if 𝐷is aright AWN-injective ring, so is 𝑒𝐷𝑒for 𝑒2=𝑒∈𝑅satisfying𝐷𝑒𝐷=𝑒. Also prove that 𝐷is reduced, and GW𝜋-reguler ring, if 𝐷is a weak symmetric and whose every simple right 𝐷-moduleis AWN-injective ring.

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On GAN-injective Rings

Jan 6, 2023

Journal Al-Rafidain Journal of Computer Sciences and Mathematics (RJCM)

publisher hazem tallat

Volume Vol. 17, No. 1

If for any maximal right ideal P of B and ,aB/ aP is almost N-injective, then a ring B is said to be right generalized almost N-injective. In this article, we present some significant findings that are known for right almost N-injective rings and demonstrate that they hold for right generalized almost N-injective rings. At the same time, we study the case in which every S.S.Right B-module is generalized almost Ninjective

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On Weakly AGP-injective Rings

Apr 12, 2013

Journal Australian Journal of Basic and Applied Sciences

publisher hazem tallat

In (Stanley and Zhou,1998), introduced a class of AGP-injective rings, following this a ring R is called right AGP-injective if, for any a∈R, there exists n>1 such that an ≠ 0 and Ran is a direct summand of ℓ r(an ). In this paper we give a generalization of right AGP-injective rings, we introduced the notion of right weakly AGP-injective rings, that is mean for any maximal right ideal M of R and any a∈M, aR/aM is AGP-injective. Some important results which are known for right AGP-injective rings are shown to holds for right WAGP-injective rings.

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