On pseudo 2-prime ideals and almost valuation domains

摘要

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let be a commutative ring with a nonzero identity. A proper ideal of is said to be a pseudo 2-prime ideal if whenever for some , then or for some . Various examples and properties of pseudo 2-prime ideals are given. We also characterize pseudo 2-prime ideals of PID's and von Neumann regular rings. Finally, we use pseudo 2-prime ideals to characterize almost valuation domains (AV-domains).