Duplication of a module along an ideal
type: Item
instance of: scholarly article
title: Duplication of a module along an ideal
zbMATH Open document ID: 1399.13011
author: El Mehdi Bouba
author: Mohammed Tamekkante
author: Najib Mahdou
published in: Acta Mathematica Hungarica
publication date: 2018-03-14T00:00:00Z
review text: Let \(A\) be a commutative ring and let \(I\) be an ideal of \(A\). Let \(\pi : A \rightarrow A/I\) be the canonical surjection. The amalgamated duplication of \(A\) along \(I\) is the special pullback \(A \bowtie I := \pi \times_{A/I} \pi = \{ (a,a+i) \;| \;a \in A, i \in I \}\), a subring of \(A \times A\). This was introduced by D'Anna and Fontana, who studied its basic properties, and it has been applied to several topics. In this paper the authors consider some basic and homological properties of a special kind of \((A \bowtie I)\)-module called the duplication of \(M\) along \(I\), where \(M\) is an \(A\)-module. Specifically, \(M \bowtie I := \{ (m,m') \in M \times M \;| \;m-m' \in IM \}\). These results generalize some known results on amalgamated duplication of a ring along an ideal. The authors study when \(M \bowtie I\) is Noetherian, Artinian, or (Nil\(_*\))-Coherent as an \((R \bowtie I)\)-module. They also characterize when \(M \bowtie I\) is a (maximal) Cohen-Macaulay \((R \bowtie I)\)-module.
reviewed by: Juan C. Migliore
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13D07
Mathematics Subject Classification ID: 13H10
zbMATH DE Number: 6850199
zbMATH Keywords: Cohen-Macaulay module and ring
zbMATH Keywords: amalgamated duplication
MaRDI profile type: Publication
full work available at URL: s10474-017-0775-6
OpenAlex ID: W2772956236
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DOI: 10.1007/S10474-017-0775-6
description: scientific article; zbMATH DE number 6850199