{"title":"d 序列的非混合扭转和希尔伯特系数","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":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"2025-02-15\",\"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\":\"2024/10/21 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","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":"2024/10/21 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中，我们定义了与特定同调度相关的非混合扭转。我们在模块的希尔伯特系数和非混合扭转之间建立了一种联系，这种联系是相对于由 d 序列生成的参数理想而言的。作为应用，我们通过模块的深度来描述希尔伯特系数的消失。
Unmixed torsions and Hilbert coefficients of d-sequences
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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