The notion of maximal non-ϕ-pseudo-valuation ring is introduced which generalizes the
concept of maximal non-pseudo-valuation domain. The equivalence of maximal non-ϕ-PVR …

The aim of this paper is to generalize the‎‎ notion of pseudo-almost valuation domains to
arbitrary‎‎ commutative rings‎.‎ It is shown that the classes of chained rings‎‎ and pseudo …

The aim of this paper is to generalize the‎‎ notion of almost valuation domains to arbitrary
commutative‎‎ rings‎.‎ Also‎,‎ we consider relations between almost valuation rings‎ and pseudo …

Let R⊂ S be a (unital) extension of (commutative) rings. We say that R is a maximal non-
quasi-local (respectively, non-PVD) subring of S if R is not quasi-local (respectively, PVD) …

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 …

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 …

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 …

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 …

Let R be a commutative ring with 1= 0 and na positive integer. A proper ideal I of R is an n-
semiprimary ideal of R if whenever xnyn∈ I for x, y∈ R, then xn∈ I or yn∈ I. Let R be an …

The notion of maximal non-pseudovaluation subring of an integral domain is introduced and
studied. Let R⊂ S be an extension of domains. Then R is called a maximal non …