Generalization of 2-absorbing quasi primary ideals

Abstract

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