Totally reflexive modules with respect to a semidualizing bimodule

Title:

Totally reflexive modules with respect to a semidualizing bimodule

Creator:

Zhang, Zhen, Zhu, Xiaosheng, and Yan, Xiaoguang

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a2d56270-0eeb-4317-8af1-9b0ff3b97fa9
uuid:a2d56270-0eeb-4317-8af1-9b0ff3b97fa9

Subject:

semidualizing bimodule, totally reflexive module, Bass class, precover, and preenvelope

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $S$ and $R$ be two associative rings, let $ _{S}C_{R}$ be a semidualizing $(S,R)$-bimodule. We introduce and investigate properties of the totally reflexive module with respect to $_{S}C_{R}$ and we give a characterization of the class of the totally $C_{R}$-reflexive modules over any ring $R$. Moreover, we show that the totally $C_{R}$-reflexive module with finite projective dimension is exactly the finitely generated projective right $R$-module. We then study the relations between the class of totally reflexive modules and the Bass class with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting.

Language:

English

Rights:

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

Coverage:

385-402

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:2

Harvested from:

CDK

Metadata only:

false