{"title":"FINITELY GENERATED G-PROJECTIVE MODULES OVER PVMDS","authors":"Kui Hu, J. Lim, Shiqi Xing","doi":"10.4134/BKMS.B190531","DOIUrl":null,"url":null,"abstract":"Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M ⊗ RM ∗ → HomR(HomR(M,M), R) is a surjective homomorphism. Particularly, if G-gldim(R) 6 ∞ and ExtR(M,M) = 0 (i > 1), then M is projective.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"12 1","pages":"803-813"},"PeriodicalIF":0.6000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/BKMS.B190531","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let M be a finitely generated G-projective R-module over a PVMD R. We prove that M is projective if and only if the canonical map θ : M ⊗ RM ∗ → HomR(HomR(M,M), R) is a surjective homomorphism. Particularly, if G-gldim(R) 6 ∞ and ExtR(M,M) = 0 (i > 1), then M is projective.
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This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).
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