Some results on N-pure ideals

TL;DR

This paper investigates N-pure ideals in rings, providing new characterizations, identifying properties in arbitrary rings, and exploring their endomorphism rings, thus advancing understanding of their algebraic structure.

Contribution

It introduces new characterizations of N-pure ideals and studies their properties and endomorphism rings, extending previous knowledge in ring theory.

Findings

New characterizations of N-pure ideals

Identification of N-pure ideals in arbitrary rings

Results on endomorphism rings of N-pure ideals

Abstract

In this paper, we consider the N-pure notion. An ideal $I$ of a ring $R$ is said to be N-pure, if for every $a\in I$ there exists $b\in I$ such that $a(1-b)\in N(R)$, where N(R) is nil radical of $R$. We provide new characterizations for N-pure ideals. In addition, N-pure ideals of an arbitrary ring are identified. Also, some other properties of N-pure ideals are studied. finally, we prove some results about the endomorphism ring of pure and N-pure ideals.