Gorenstein Homological Properties and Quasi-Frobenius Bimodules

被引：0
|
作者：
Huang, Chaoling [1 ,2 ]
Sun, Yongliang [3 ]
Zhou, Yanbo [4 ]
机构：
[1] Hanjiang Normal Univ, Coll Math & Comp Sci, Shiyan 442000, Peoples R China
[2] Hubei Univ, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China
[3] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[4] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
来源：
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2022年 / 48卷 / 03期
关键词：
Quasi-Frobenius extension; Gorenstein projective; injective and flat dimension; Cohen-Macaulay ring; Virtually Gorenstein algebras;
D O I：
10.1007/s41980-021-00548-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish relations of Gorenstein homological properties of modules and rings linked by a fixed quasi-Frobenius bimodule. Particularly, let R subset of S be a strongly separable quasi-Frobenius extension. The left Gorenstein global dimensions and the left finitistic Gorenstein projective dimensions of rings S and R are equal. Moreover, R is left-Gorenstein (Cohen-Macaulay finite, Cohen-Macaulay free) if and only if so is S.
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页码：805 / 817
页数：13
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