Generalization of 2-absorbing quasi primary ideals

Abstract

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)→ L(R)\ \ is a function. A proper ideal I of R is called a φ-2-absorbing quasiprimary ideal of R if a,b,c∈ R and whenever abc∈ I-φ(I), then either ab∈I or ac∈I or bc∈I. In addition to giving many properties of φ-2-absorbing quasi primary ideals, we also use them to characterize von Neumann regular rings.