2020/05/18 by Ugurlu, Emel Aslankarayigit, Tekir, Unsal, Koc, Suat
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.08709
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.