Trivial extensions satisfying certain valuation-like properties
DE Dobbs, A El Khalfi, N Mahdou - Communications in Algebra, 2019 - Taylor & Francis
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 …
ring, a pseudo-valuation ring and a pseudo-almost valuation ring between a commutative …
Almost valuation rings
R Jahani-Nezhad, F Khoshayand - Bulletin of the Iranian …, 2017 - bims.iranjournals.ir
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 …
commutative rings. Also, we consider relations between almost valuation rings and pseudo …
Strongly primary ideals in rings with zero-divisors
A El Khalfi, N Mahdou, Y Zahir - Quaestiones Mathematicae, 2021 - Taylor & Francis
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 …
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 …
Classes of trivial ring extensions and amalgamations subject to pseudo-almost valuation condition
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 …
short) to various context of commutative ring extensions such as power series ring, trivial …
Almost valuation property in bi-amalgamations and pairs of rings
NO Azaiez, MAS Moutui - Journal of Algebra and Its Applications, 2019 - World Scientific
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 …
ring extensions such as bi-amalgamations and pairs of rings. Namely, Sec. 2 studies the …
On almost valuation ring pairs
N Jarboui, DE Dobbs - Journal of Algebra and Its Applications, 2021 - World Scientific
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 …
called an almost valuation (AV)-ring pair if each element of [A, B] is an AV-ring. Many results …
[PDF][PDF] GRADED PSEUDO-VALUATION RINGS
FZ Guissi, H Kim, N Mahdou - researchgate.net
Let R=⊕ α∈ Γ Rα 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 …
homogeneous prime ideal P of R is said to be strongly homogeneous prime if aP and bR are …