{"title":"Local Cohen–Macaulay DG-Modules","authors":"Xiaoyan Yang, Yanjie Li","doi":"10.1007/s10485-022-09703-y","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>A</i> be a commutative noetherian local DG-ring with bounded cohomology. For local Cohen–Macaulay DG-modules with constant amplitude, we obtain an explicit formula for the sequential depth, show that Cohen–Macaulayness is stable under localization and give several equivalent definitions of maximal local Cohen–Macaulay DG-modules over local Cohen–Macaulay DG-rings. We also provide some characterizations of Gorenstein DG-rings by projective and injective dimensions of DG-modules.\n</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"31 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-022-09703-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Categorical Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10485-022-09703-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let A be a commutative noetherian local DG-ring with bounded cohomology. For local Cohen–Macaulay DG-modules with constant amplitude, we obtain an explicit formula for the sequential depth, show that Cohen–Macaulayness is stable under localization and give several equivalent definitions of maximal local Cohen–Macaulay DG-modules over local Cohen–Macaulay DG-rings. We also provide some characterizations of Gorenstein DG-rings by projective and injective dimensions of DG-modules.
期刊介绍：
Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.
Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
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