Back to Search
Start Over
Bounds on the minimal number of generators of the dual module
- Source :
- Journal of Algebra and Its Applications.
- Publication Year :
- 2023
- Publisher :
- World Scientific Pub Co Pte Ltd, 2023.
-
Abstract
- Let [Formula: see text] be a Cohen–Macaulay local ring. Let [Formula: see text] be a finitely generated [Formula: see text]-module and let [Formula: see text] denote the [Formula: see text]-dual of [Formula: see text]. Furthermore, if [Formula: see text] is a maximal Cohen–Macaulay [Formula: see text]-module, then we prove that [Formula: see text], where [Formula: see text] is the cardinality of a minimal generating set of [Formula: see text] as an [Formula: see text]-module and [Formula: see text] is the multiplicity of the local ring [Formula: see text]. Furthermore, if [Formula: see text] is a reflexive [Formula: see text]-module then [Formula: see text]. 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.
- Subjects :
- Algebra and Number Theory
Applied Mathematics
Subjects
Details
- ISSN :
- 17936829 and 02194988
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra and Its Applications
- Accession number :
- edsair.doi...........47275230157c480fd67b049c4ecf41dd