{"title":"A classification of some thick subcategories in locally noetherian Grothendieck categories","authors":"Kaili Wu, Xinchao Ma","doi":"10.1017/s001708952300040x","DOIUrl":null,"url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300040X_inline1.png\" /> <jats:tex-math> $\\mathcal{A}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a locally noetherian Grothendieck category. We classify all full subcategories of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S001708952300040X_inline2.png\" /> <jats:tex-math> $\\mathcal{A}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> which are thick and closed under taking arbitrary direct sums and injective envelopes by injective spectrum. This result gives a generalization from the commutative noetherian ring to the locally noetherian Grothendieck category.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"82 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasgow Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s001708952300040x","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 $\mathcal{A}$ be a locally noetherian Grothendieck category. We classify all full subcategories of $\mathcal{A}$ which are thick and closed under taking arbitrary direct sums and injective envelopes by injective spectrum. This result gives a generalization from the commutative noetherian ring to the locally noetherian Grothendieck category.
期刊介绍:
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