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 R α be a commutative ring graded by an arbitrary torsionless monoid Γ. A
homogeneous prime ideal P of R is said to be strongly homogeneous prime if aP and bR are …

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 A be an integral domain with quotient field KA Badawi and E. Houston called a strongly
primary ideal I of A if whenever x, y∈ K and xy∈ I, we have x∈ I or y∈ I for some n≥ 1. In …

This paper studies the transfer of pseudo-almost valuation property (PAVR property for
short) to various context of commutative ring extensions such as power series ring, trivial …

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 …