Bounds on the minimal number of generators of the dual module
Article Type
Research Article
Publication Title
Journal of Algebra and its Applications
Abstract
Let (A, A) be a Cohen-Macaulay local ring. Let M be a finitely generated A-module and let M∗ denote the A-dual of M. Furthermore, if M∗ is a maximal Cohen-Macaulay A-module, then we prove that μA(M∗) ≤ μ A(M)e(A), where μA(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 M is a reflexive A-module then μA(M) e(A) ≤ μA(M∗). As an application, we study the bound on the minimal number of generators of specific modules over two-dimensional normal local rings. We also mention some relevant examples.
DOI
https://10.1142/S0219498824501846
Publication Date
1-1-2023
Recommended Citation
Mishra, Ankit and Mondal, Dibyendu, "Bounds on the minimal number of generators of the dual module" (2023). Journal Articles. 3953.
https://digitalcommons.isical.ac.in/journal-articles/3953
