Trivial extensions defined by coherent-like conditions

Salah Eddine Kabbaj; Najib Mahdou

doi:10.1081/AGB-200027791

Trivial extensions defined by coherent-like conditions

Salah Eddine Kabbaj^*, Najib Mahdou

^*Corresponding author for this work

Department of Mathematics

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

159 Scopus citations

Abstract

This paper investigates coherent-like conditions and related properties that a trivial extension R:= A ∝ E might inherit from the ring A for some classes of modules E. It captures previous results dealing primarily with coherence, and also establishes satisfactory analogues of well-known coherence-like results on pullback constructions. Our results generate new families of examples of rings (with zerodivisors) subject to a given coherent-like condition.

Original language	English
Pages (from-to)	3937-3953
Number of pages	17
Journal	Communications in Algebra
Volume	32
Issue number	10
DOIs	https://doi.org/10.1081/AGB-200027791
State	Published - 2004

Bibliographical note

Funding Information:
The first author was supported by KFUPM under project #MS/TRIVIAL/224.

Keywords

(n, d)-ring
Coherence
Finite conductor ring
G-GCD ring
Pullback
Quasi-coherent ring
Trivial extension
n-coherence

ASJC Scopus subject areas

Algebra and Number Theory

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10.1081/AGB-200027791

Cite this

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title = "Trivial extensions defined by coherent-like conditions",

abstract = "This paper investigates coherent-like conditions and related properties that a trivial extension R:= A ∝ E might inherit from the ring A for some classes of modules E. It captures previous results dealing primarily with coherence, and also establishes satisfactory analogues of well-known coherence-like results on pullback constructions. Our results generate new families of examples of rings (with zerodivisors) subject to a given coherent-like condition.",

keywords = "(n, d)-ring, Coherence, Finite conductor ring, G-GCD ring, Pullback, Quasi-coherent ring, Trivial extension, n-coherence",

author = "Kabbaj, \{Salah Eddine\} and Najib Mahdou",

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AU - Kabbaj, Salah Eddine

AU - Mahdou, Najib

N1 - Funding Information: The first author was supported by KFUPM under project #MS/TRIVIAL/224.

PY - 2004

Y1 - 2004

N2 - This paper investigates coherent-like conditions and related properties that a trivial extension R:= A ∝ E might inherit from the ring A for some classes of modules E. It captures previous results dealing primarily with coherence, and also establishes satisfactory analogues of well-known coherence-like results on pullback constructions. Our results generate new families of examples of rings (with zerodivisors) subject to a given coherent-like condition.

AB - This paper investigates coherent-like conditions and related properties that a trivial extension R:= A ∝ E might inherit from the ring A for some classes of modules E. It captures previous results dealing primarily with coherence, and also establishes satisfactory analogues of well-known coherence-like results on pullback constructions. Our results generate new families of examples of rings (with zerodivisors) subject to a given coherent-like condition.

KW - (n, d)-ring

KW - Coherence

KW - Finite conductor ring

KW - G-GCD ring

KW - Pullback

KW - Quasi-coherent ring

KW - Trivial extension

KW - n-coherence

UR - https://www.scopus.com/pages/publications/22744436762

U2 - 10.1081/AGB-200027791

DO - 10.1081/AGB-200027791

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VL - 32

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EP - 3953

JO - Communications in Algebra

JF - Communications in Algebra

IS - 10

ER -

Trivial extensions defined by coherent-like conditions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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