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=⊕ α∈ Γ Rα be a commutative ring graded by an arbitrary torsionless monoid Γ. We
say that R is graded almost valuation ring (gr AV-ring) if for every two homogeneous …

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let R
be a commutative ring with a nonzero identity. A proper ideal P of R is said to be a pseudo 2 …

This paper examines the transfer of the almost valuation property to various constructions of
ring extensions such as bi-amalgamations and pairs of rings. Namely, Sec. 2 studies the …

If A⊆ B are (commutative) rings,[A, B] denotes the set of intermediate rings and (A, B) is
called an almost valuation (AV)-ring pair if each element of [A, B] is an AV-ring. Many results …

Let R be a commutative ring and S be a multiplicative subset of R. In this paper, we
introduce and study an S-version of valuation rings, that is called the notion of S-valuation …