{"title":"On the Triviality of Gorenstein $$(\\mathcal {L}, \\mathcal {A})$$ -Modules","authors":"Xinxin Wang","doi":"10.1007/s41980-024-00871-2","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\((\\mathcal {L}, \\mathcal {A})\\)</span> be a bi-complete duality pair. We consider when the relative Gorenstein modules with respect to such a duality pair coincide with the classical homological modules. As applications, we characterize (weak) global dimension via such a duality pair, characterize strongly CM-freeness of flat-typed <span>\\((\\mathcal {L}, \\mathcal {A})\\)</span>-Gorenstein rings and obtain the compactly-generatedness of some relative derived categories. Applying the results into frequent duality pairs, our results unify the corresponding results for Gorenstein AC-modules and Ding modules.\n</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-024-00871-2","RegionNum":4,"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
Let \((\mathcal {L}, \mathcal {A})\) be a bi-complete duality pair. We consider when the relative Gorenstein modules with respect to such a duality pair coincide with the classical homological modules. As applications, we characterize (weak) global dimension via such a duality pair, characterize strongly CM-freeness of flat-typed \((\mathcal {L}, \mathcal {A})\)-Gorenstein rings and obtain the compactly-generatedness of some relative derived categories. Applying the results into frequent duality pairs, our results unify the corresponding results for Gorenstein AC-modules and Ding modules.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
