Linkage of ideals in integral domains
type: Item
instance of: scholarly article
title: Linkage of ideals in integral domains
zbMATH Open document ID: 1468.13048
published in: Algebras and Representation Theory
publication date: 2021-07-26T00:00:00Z
review text: Let \(R\) be a commutative ring with identity. Recall the following definitions: (1) Let \(I,J\) and \(A\) be ideals of \(R\). Then \(I\) and \(J\) are linked over \(A\) if \(A\subseteq I\cap J\), \(I=(A:J)\) and \(J=(A:I)\). (2) \(R\) has the linkage property if any two distinct nonzero ideals of \(R\) are linked. (3) \(R\) has the finite linkage property if any two distinct nonzero finitely generated ideals of \(R\) are linked. (4) \(R\) has the primary linkage property if any two distinct nonzero primary ideals of \(R\) are linked. The main results of this paper are: (1) A domain has the finite linkage property (resp. linkage property) if and only if it is Prüfer (resp. almost Dedekind). (2) A Noetherian domain (resp. one-dimensional locally Noetherian domain) has the primary linkage property if and only if it is Dedekind (resp. almost Dedekind). Many interesting examples are given.
reviewed by: Ali Benhissi
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13F30
Mathematics Subject Classification ID: 13D05
zbMATH DE Number: 7374844
zbMATH Keywords: linkage
zbMATH Keywords: Prüfer domain
zbMATH Keywords: almost Dedekind domain
zbMATH Keywords: Dedekind domain
zbMATH Keywords: Noetherian domain
zbMATH Keywords: valuation domain
zbMATH Keywords: divisoriality
zbMATH Keywords: invertibility
author: S. Kabbaj
author: A. Mimouni
MaRDI profile type: Publication
full work available at URL: s10468-020-09969-7
OpenAlex ID: W3025264921
cites work: Q5837419
cites work: Q5837420
cites work: Residual intersections in Cohen-Macaulay rings
cites work: The Structure of an Even Liaison Class
cites work: Linkage of modules over Cohen-Macaulay rings
cites work: Linkage of finite Gorenstein dimension modules
cites work: Linkage of modules and the Serre conditions
cites work: Reductions of Ideals in Commutative Rings
cites work: Reductions of Ideals in Prufer Domains
cites work: \(\star\)-reductions of ideals and Prüfer \(v\)-multiplication domains
cites work: Linkage and the Koszul Homology of Ideals
cites work: Numerical invariants of liaison classes
cites work: Q3414477
cites work: Divisor Class Groups and Deformations
cites work: The structure of linkage
cites work: Algebraic linkage
cites work: Minimal linkage and the Gorenstein locus of an ideal
cites work: Liaison of monomial ideals
cites work: Perfect linkage of Cohen-Macaulay modules over Cohen-Macaulay rings
cites work: Core of ideals in integral domains
cites work: Q4049183
cites work: Deformation and Linkage of Gorenstein Algebras
cites work: Tight double linkage of Gorenstein algebras
cites work: Linkage theory for algebras with pure resolutions
cites work: Linkage of modules.
cites work: Introduction to liaison theory and deficiency modules
cites work: Q4550586
cites work: Even liaison classes generated by Gorenstein linkage
cites work: Liaison classes of modules
cites work: Q5829838
cites work: Liaison des variétés algébriques. I
cites work: Liaison among curves in \(\mathbb{P}^3\)
cites work: Notes on liaison and duality
cites work: Linkage of Cohen-Macaulay modules over a Gorenstein ring
DOI: 10.1007/S10468-020-09969-7
Recommended article: LINKAGE OF IDEALS OVER A MODULE
Recommended article: Linkage and sums of ideals
Recommended article: Sums of Linked Ideals
Recommended article: Links of prime ideals
Recommended article: Core of ideals in integral domains
Recommended article: Linkage and Strongly Generalized Cohen–Macaulay Ideals
Recommended article: Rings of invariants and linkage of determinantal ideals
Recommended article: Linkage by generically Gorenstein, Cohen-Macaulay ideals
Recommended article: INTEGRAL AND COMPLETE INTEGRAL CLOSURES OF IDEALS IN INTEGRAL DOMAINS
Recommended article: Links of prime ideals and their Rees algebras
description: scientific article; zbMATH DE number 7374844