On some valuation-like rings in certain ring extensions

Abdeslam Mimouni; Omar Ouzzaouit; Ali Tamoussit

doi:10.1007/s11587-025-01004-5

On some valuation-like rings in certain ring extensions

Abdeslam Mimouni
, Omar Ouzzaouit^*
, Ali Tamoussit

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A commutative ring R with identity is called an SV-ring (respectively, SPV-ring) if the integral domain R/P is valuation (respectively, pseudo-valuation), for all prime ideals P of R. The main goal of this paper is to examine the behavior of the (locally) SV-ring and SPV-ring properties in various distinguished constructions.

Original language	English
Pages (from-to)	391-403
Number of pages	13
Journal	Ricerche di Matematica
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s11587-025-01004-5
State	Published - Feb 2026

Bibliographical note

Publisher Copyright:
© Università degli Studi di Napoli "Federico II" 2025.

Keywords

Nagata ring
Polynomial ring
Valuation domain

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1007/s11587-025-01004-5

Cite this

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abstract = "A commutative ring R with identity is called an SV-ring (respectively, SPV-ring) if the integral domain R/P is valuation (respectively, pseudo-valuation), for all prime ideals P of R. The main goal of this paper is to examine the behavior of the (locally) SV-ring and SPV-ring properties in various distinguished constructions.",

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AU - Ouzzaouit, Omar

AU - Tamoussit, Ali

N1 - Publisher Copyright: © Università degli Studi di Napoli "Federico II" 2025.

PY - 2026/2

Y1 - 2026/2

N2 - A commutative ring R with identity is called an SV-ring (respectively, SPV-ring) if the integral domain R/P is valuation (respectively, pseudo-valuation), for all prime ideals P of R. The main goal of this paper is to examine the behavior of the (locally) SV-ring and SPV-ring properties in various distinguished constructions.

AB - A commutative ring R with identity is called an SV-ring (respectively, SPV-ring) if the integral domain R/P is valuation (respectively, pseudo-valuation), for all prime ideals P of R. The main goal of this paper is to examine the behavior of the (locally) SV-ring and SPV-ring properties in various distinguished constructions.

KW - Nagata ring

KW - Polynomial ring

KW - Valuation domain

UR - https://www.scopus.com/pages/publications/105015572039

U2 - 10.1007/s11587-025-01004-5

DO - 10.1007/s11587-025-01004-5

M3 - Article

AN - SCOPUS:105015572039

SN - 0035-5038

VL - 75

SP - 391

EP - 403

JO - Ricerche di Matematica

JF - Ricerche di Matematica

IS - 1

ER -

On some valuation-like rings in certain ring extensions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this