Generalization of 2-absorbing quasi primary ideals

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

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