戈伦斯坦投影模组内态代数的同调维数

Pub Date : 2024-08-28 DOI:10.21136/cmj.2024.0199-23

Aiping Zhang, Xueping Lei

{"title":"戈伦斯坦投影模组内态代数的同调维数","authors":"Aiping Zhang, Xueping Lei","doi":"10.21136/cmj.2024.0199-23","DOIUrl":null,"url":null,"abstract":"Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E, M be a Gorenstein projective A-module and B = EndAM. We give an upper bound for the finitistic dimension of B in terms of homological data of M. Furthermore, if A is n-Gorenstein for 2 ⩽ n < ∞, then we show the global dimension of B is less than or equal to n plus the B-projective dimension of HomA(M, E). As an application, the global dimension of EndAE is less than or equal to n.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Homological dimensions for endomorphism algebras of Gorenstein projective modules\",\"authors\":\"Aiping Zhang, Xueping Lei\",\"doi\":\"10.21136/cmj.2024.0199-23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E, M be a Gorenstein projective A-module and B = EndAM. We give an upper bound for the finitistic dimension of B in terms of homological data of M. Furthermore, if A is n-Gorenstein for 2 ⩽ n < ∞, then we show the global dimension of B is less than or equal to n plus the B-projective dimension of HomA(M, E). As an application, the global dimension of EndAE is less than or equal to n.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/cmj.2024.0199-23\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/cmj.2024.0199-23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

设 A 是具有戈伦斯坦-奥斯兰德生成器 E 的 CM 有限阿尔丁代数，M 是戈伦斯坦投影 A 模块，B = EndAM。此外，如果 A 在 2 ⩽ n < ∞ 时是 n-Gorenstein 的，那么我们将证明 B 的全局维度小于或等于 n 加上 HomA(M, E) 的 B 投影维度。作为应用，EndAE 的全局维度小于或等于 n。

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

Homological dimensions for endomorphism algebras of Gorenstein projective modules

Let A be a CM-finite Artin algebra with a Gorenstein-Auslander generator E, M be a Gorenstein projective A-module and B = End_AM. We give an upper bound for the finitistic dimension of B in terms of homological data of M. Furthermore, if A is n-Gorenstein for 2 ⩽ n < ∞, then we show the global dimension of B is less than or equal to n plus the B-projective dimension of Hom_A(M, E). As an application, the global dimension of End_AE is less than or equal to n.

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