{"title":"FP-injective dimensions and Gorenstein homology","authors":"Gang Yang, Junpeng Wang","doi":"10.1017/S0013091522000542","DOIUrl":null,"url":null,"abstract":"Abstract Let $R$ be a left coherent ring. It is proven that if an $R$-module $M$ has a finite FP-injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the projective (resp. flat) dimension coincide. Also, we obtain that the pair ($\\mathcal {GP},\\, \\mathcal {GP}^{\\perp }$) forms a projective cotorsion pair under some mild conditions.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/S0013091522000542","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Let $R$ be a left coherent ring. It is proven that if an $R$-module $M$ has a finite FP-injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the projective (resp. flat) dimension coincide. Also, we obtain that the pair ($\mathcal {GP},\, \mathcal {GP}^{\perp }$) forms a projective cotorsion pair under some mild conditions.
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