On n-semiprimary ideals and n-pseudo valuation domains

Abstract

Let R be a commutative ring with and n a positive integer. A proper ideal I of R is an n-semiprimary ideal of R if whenever for then or Let R be an integral domain with quotient field K. A proper ideal I of R is an n-powerful ideal of R if whenever for then or and I is an n-powerful semiprimary ideal of R if whenever for then or If every prime ideal of R is an n-powerful semiprimary ideal of R, then R is an n-pseudo-valuation domain (n-PVD). In this paper, we study the above concepts and relate them to several generalizations of pseudo-valuation domains.