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) …

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 …

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 …

In this paper, we extend the concept of strong extensions of domains to the context of
(commutative) rings with zero-divisors. Let T be an extension ring of a ring R. A prime ideal P …

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 …

It is proved that if R⊂ T are going-down domains such that Spec (R)= Spec (T) as sets (for
instance, a proper field extension) and M denotes the common maximal ideal of R and T …

Using the notion of cyclically pure injective modules, a characterization of rings which are
locally valuation rings is established. As applications, new characterizations of Prüfer …

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 …

Let R, S be two rings. We say that R is a valuation subring of S (R is a VD in S, for short) if R
is a proper subring of S and whenever x∈ S, we have x∈ R or x− 1∈ R. We denote by Nu …

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 …