{"title":"Unmixed torsions and Hilbert coefficients of d-sequences","authors":"Pham Hong Nam","doi":"10.1016/j.jalgebra.2024.10.014","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we define an unmixed torsion associated with a certain cohomological degree. We establish a connection between the Hilbert coefficients and the unmixed torsions of the module with respect to a parameter ideal generated by a <em>d</em>-sequence. As an application, we characterize the vanishing of the Hilbert coefficients through the depth of the module.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"664 ","pages":"Pages 738-755"},"PeriodicalIF":0.8000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324005611","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we define an unmixed torsion associated with a certain cohomological degree. We establish a connection between the Hilbert coefficients and the unmixed torsions of the module with respect to a parameter ideal generated by a d-sequence. As an application, we characterize the vanishing of the Hilbert coefficients through the depth of the module.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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