On Almost Valuation and Almost Bézout Rings

Najib Mahdou; Abdeslam Mimouni; Moutu Abdou Salam Moutui

doi:10.1080/00927872.2014.897586

On Almost Valuation and Almost Bézout Rings

Najib Mahdou
, Abdeslam Mimouni^*
, Moutu Abdou Salam Moutui

^*Corresponding author for this work

Department of Mathematics

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

16 Scopus citations

Abstract

In this paper we extend the notion of almost valuation and almost Bézout domains to arbitrary commutative rings, and we investigate the transfer of these properties to trivial ring extensions and amalgamated algebras along an ideal. Our aim is to provide new classes of commutative rings satisfying these properties. As an immediate consequence, we show the failure of Anderson-Zafrullah's theorem on the integral closure of an almost valuation domain beyond the context of integral domains.

Original language	English
Pages (from-to)	297-308
Number of pages	12
Journal	Communications in Algebra
Volume	43
Issue number	1
DOIs	https://doi.org/10.1080/00927872.2014.897586
State	Published - Jan 2015

Bibliographical note

Funding Information:
This work is supported by KFUPM under Project RG 1307-1& RG 1307-2.

Keywords

Almost Bézout rings
Almost valuation rings
Amalgamated algebra along an ideal
Amalgamated duplication
Trivial extensions

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2014.897586

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title = "On Almost Valuation and Almost B{\'e}zout Rings",

abstract = "In this paper we extend the notion of almost valuation and almost B{\'e}zout domains to arbitrary commutative rings, and we investigate the transfer of these properties to trivial ring extensions and amalgamated algebras along an ideal. Our aim is to provide new classes of commutative rings satisfying these properties. As an immediate consequence, we show the failure of Anderson-Zafrullah's theorem on the integral closure of an almost valuation domain beyond the context of integral domains.",

keywords = "Almost B{\'e}zout rings, Almost valuation rings, Amalgamated algebra along an ideal, Amalgamated duplication, Trivial extensions",

author = "Najib Mahdou and Abdeslam Mimouni and \{Salam Moutui\}, \{Moutu Abdou\}",

note = "Funding Information: This work is supported by KFUPM under Project RG 1307-1\& RG 1307-2.",

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AU - Mahdou, Najib

AU - Mimouni, Abdeslam

AU - Salam Moutui, Moutu Abdou

N1 - Funding Information: This work is supported by KFUPM under Project RG 1307-1& RG 1307-2.

PY - 2015/1

Y1 - 2015/1

N2 - In this paper we extend the notion of almost valuation and almost Bézout domains to arbitrary commutative rings, and we investigate the transfer of these properties to trivial ring extensions and amalgamated algebras along an ideal. Our aim is to provide new classes of commutative rings satisfying these properties. As an immediate consequence, we show the failure of Anderson-Zafrullah's theorem on the integral closure of an almost valuation domain beyond the context of integral domains.

AB - In this paper we extend the notion of almost valuation and almost Bézout domains to arbitrary commutative rings, and we investigate the transfer of these properties to trivial ring extensions and amalgamated algebras along an ideal. Our aim is to provide new classes of commutative rings satisfying these properties. As an immediate consequence, we show the failure of Anderson-Zafrullah's theorem on the integral closure of an almost valuation domain beyond the context of integral domains.

KW - Almost Bézout rings

KW - Almost valuation rings

KW - Amalgamated algebra along an ideal

KW - Amalgamated duplication

KW - Trivial extensions

UR - https://www.scopus.com/pages/publications/84905241492

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DO - 10.1080/00927872.2014.897586

M3 - Article

AN - SCOPUS:84905241492

SN - 0092-7872

VL - 43

SP - 297

EP - 308

JO - Communications in Algebra

JF - Communications in Algebra

IS - 1

ER -

On Almost Valuation and Almost Bézout Rings

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this