We define an r-pseudo-valuation ring (r-PVR) and study some properties of r-PVRs. It is
proved that R is a-PVR if and only if N (R) is a divided prime ideal of R and R/N (R) is a PVD …

Recall that a commutative ring R is said to be a pseudo-valuation ring (PVR) if every prime
ideal of R is strongly prime. We say that a commutative ring R is near pseudo-valuation ring …

The purpose of this paper is to introduce a new class of rings that is closely related to the
class of pseudo valuation domains. Let R be a commutative ring and P the minimal divided …

A commutative ring R with identity 1= 0 is called a pseudovaluation ring (PVR) if for every a,
b∈ R, either a| b in R or b| ac in R for every nonunit c of R. Also, R is called a Φ− pseudo …

Let R be a commutative ring with 1 and T (R) be its total quotient ring such that Nil (R) is a
divided prime ideal of R. Then R is called a 4-chained ring (4-CR) if for every x, y R Nil (R) …

A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable
for all a, b ε A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal …

A prime ideal P of a commutative ring R with identity is called strongly prime if aP and bR are
comparable for every a, b in R. If every prime ideal of R is strongly prime, then R is called a …

Chonbuk National University, Chonju, 561-756, Korea. Page 1 Honann Mathematical J. 23(2001),
No. 1, pp. 21–28 PSEUDO VALUATION RINGS YONG HwAN CHO Dept. of Mathematics …

In this article, we study the possible transfer of the properties of being an almost valuation
ring, a pseudo-valuation ring and a pseudo-almost valuation ring between a commutative …

Throughout this paper, all rings are commutative with identity and if R is a ring, then Z (R)
denotes the set of zerodivisors of R and Nil (R) denotes the set of nilpotent elements of R …