{"title":"On the nonrigidity of trace modules","authors":"H. Lindo","doi":"10.1216/jca.2022.14.277","DOIUrl":null,"url":null,"abstract":"We establish a link between trace modules and rigidity in modules over Noetherian rings. We identify classes of modules which must have self-extensions and use the theory of trace ideals to verify the Auslander-Reiten conjecture for syzygies of ideals over Artinian Gorenstein rings.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1216/jca.2022.14.277","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We establish a link between trace modules and rigidity in modules over Noetherian rings. We identify classes of modules which must have self-extensions and use the theory of trace ideals to verify the Auslander-Reiten conjecture for syzygies of ideals over Artinian Gorenstein rings.
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