PVMDS上有限生成的g -射影模

IF 0.6 4区数学 Q3 MATHEMATICS Bulletin of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/BKMS.B190531

Kui Hu, J. Lim, Shiqi Xing

{"title":"PVMDS上有限生成的g -射影模","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":"{\"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}","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}

引用次数: 0

摘要

设M是PVMD R上有限生成的g -射影R模，证明M是射影当且仅当正则映射θ: M⊗RM∗→HomR(HomR(M,M)， R)是满射同态。特别地，如果G-gldim(R) 6∞且ExtR(M,M) = 0 (i > 1)，则M是射影。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

FINITELY GENERATED G-PROJECTIVE MODULES OVER PVMDS

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： 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).

期刊最新文献

Invariant mean value property and $\mathcal M$-harmonicity on the half-space The convex hull of three boundary points in complex hyperbolic space On ampliation quasiaffine transforms of operators On nonlinear elliptic equations with singular lower order term Zero mean curvature surfaces in isotropic three-space