Generalization of 2-absorbing quasi primary ideals

TL;DR

This paper introduces and explores the properties of a new class of ideals called $$-2-absorbing quasi primary ideals in commutative rings, providing characterizations and applications to von Neumann regular rings.

Contribution

It defines $$-2-absorbing quasi primary ideals and investigates their properties, offering new insights and characterizations in ring theory.

Findings

Established properties of $$-2-absorbing quasi primary ideals.

Characterized von Neumann regular rings using these ideals.

Abstract

In this article, we introduce and study the concept of $\phi$-2-absorbing quasi primary ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $L(R)$ be the lattice of all ideals of $R$. Suppose that $\phi:L(R)\rightarrow L(R)\cup\left\{ \emptyset\right\} $ is a function. A proper ideal $I$ of $R$ is called a $\phi$-2-absorbing quasiprimary ideal of $R$ if $a,b,c\in R$ and whenever $abc\in I-\phi(I),$ then either $ab\in\sqrt{I}$ or $ac\in\sqrt{I}$ or $bc\in\sqrt{I}$. In addition to giving many properties of $\phi$-2-absorbing quasi primary ideals, we also use them to characterize von Neumann regular rings.