Bounds on the minimal number of generators of the dual module
type: Item
instance of: scholarly article
title: Bounds on the minimal number of generators of the dual module
author: Ankit Mishra
author: Dibyendu Mondal
published in: Journal of Algebra and its Applications
publication date: 2024-09-19T00:00:00Z
review text: Let \((A,\mathfrak{m})\) be a Cohen-Macaulay local ring, \(M\) a finitely generated \(A\)-module and \(M^*=\Hom_A(M,A)\). In the paper under review, the authors study bounds on the minimal number of generators of \(M^*\). They prove that if \(M^*\) is a maximal Cohen-Macaulay \(A\)-module, then \(\mu_A(M^*)\leqslant\mu_A(M)e(A)\), where \(\mu_A(M)\) is the cardinality of a minimal generating set of \(M\) as an \(A\)-module and \(e(A)\) is the multiplicity of the local ring \(A\). Furthermore, if the natural map \(M\rightarrow M^{**}\) is an isomorphism, they show that \(\mu_A(M)/e(A)\) is a lower bound for \(\mu_A(M^*)\). As an application, they study the bounds on the minimal number of generators of specific modules over two-dimensional normal local rings.
reviewed by: Mohammad-Reza Doustimehr
Mathematics Subject Classification ID: 13E15
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 7916059
zbMATH Keywords: minimal number of generators
zbMATH Keywords: reflexive module
zbMATH Keywords: Cohen-Macaulay
zbMATH Keywords: quotient singularity
MaRDI profile type: Publication
cites work: On Isolated Rational Singularities of Surfaces
cites work: Rational Singularities and Almost Split Sequences
cites work: Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
cites work: On Auslander modules of normal surface singularities
cites work: Maximally generated Cohen-Macaulay modules.
cites work: Rationale Singularitäten komplexer Flächen
cites work: Q4274969
cites work: On the number of generators of modules of homomorphisms
cites work: On reflexive and 𝐼-Ulrich modules over curve singularities
cites work: Reflexive modules on quotient surface singularities.
cites work: On the number of generators of the module of derivations and multiplicity of certain rings
cites work: On minimum number of generators for some derivation modules
cites work: Number of generators of derivation modules of some hypersurfaces
cites work: Q3781844
cites work: Note on multiplicities of ideals
cites work: Lech's conjecture in dimension three
cites work: Almost Split Sequences and Zariski Differentials
cites work: Q3992979
cites work: Q3248050
cites work: Q5542855
cites work: Construction géométrique de la correspondance de McKay
cites work: Reflexive modules
cites work: Reflexive Modules Over Gorenstein Rings
cites work: Reflexive modules on quotient surface singularities
cites work: The Fundamental Module of a Normal Local Domain of Dimension 2
DOI: 10.1142/S0219498824501846
description: scientific article; zbMATH DE number 7916059