A generalization of the Auslander transpose and the generalized Gorenstein dimension

Title:

A generalization of the Auslander transpose and the generalized Gorenstein dimension

Creator:

Geng, Yuxian

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e0226d94-d832-46b3-a4b5-b8c255fce7ed
uuid:e0226d94-d832-46b3-a4b5-b8c255fce7ed

Subject:

transpose, semidualizing module, generalized Gorenstein dimension, depth, and Auslander-Bridger formula

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $R$ be a left and right Noetherian ring and $C$ a semidualizing $R$-bimodule. We introduce a transpose ${\rm Tr_{c}}M$ of an $R$-module $M$ with respect to $C$ which unifies the Auslander transpose and Huang's transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use ${\rm Tr_{c}}M$ to develop further the generalized Gorenstein dimension with respect to $C$. Especially, we generalize the Auslander-Bridger formula to the generalized Gorenstein dimension case. These results extend the corresponding ones on the Gorenstein dimension obtained by Auslander in M. Auslander, M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. vol. 94, Amer. Math. Soc., Providence, RI, 1969.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

143-156

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:1

Harvested from:

CDK

Metadata only:

false