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 …

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 …

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 …

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) …

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 paper we extend the notion of almost valuation and almost Bézout domains to
arbitrary commutative rings, and we investigate the transfer of these properties to trivial ring …

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 …

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 …

Valuation domains have been extended in the non-commutative case by several authors,
giving rise to the so called generalized valuation rings, that is, rings whose lattice of right …