Geodesic
Totally reflexive modules with respect to a semidualizing bimodule
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 385-402.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.1007/s10587-013-0024-2
Classification : 16D20, 16D40, 16E05, 16E10, 16E30
Keywords: semidualizing bimodule; totally reflexive module; Bass class; precover; preenvelope 
@article{10_1007_s10587_013_0024_2,
     author = {Zhang, Zhen and Zhu, Xiaosheng and Yan, Xiaoguang},
     title = {Totally reflexive modules with respect to a semidualizing bimodule},
     journal = {Czechoslovak Mathematical Journal},
     pages = {385--402},
     publisher = {mathdoc},
     volume = {63},
     number = {2},
     year = {2013},
     doi = {10.1007/s10587-013-0024-2},
     mrnumber = {3073965},
     zbl = {06236418},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0024-2/}
}
TY  - JOUR
AU  - Zhang, Zhen
AU  - Zhu, Xiaosheng
AU  - Yan, Xiaoguang
TI  - Totally reflexive modules with respect to a semidualizing bimodule
JO  - Czechoslovak Mathematical Journal
PY  - 2013
SP  - 385
EP  - 402
VL  - 63
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0024-2/
DO  - 10.1007/s10587-013-0024-2
LA  - en
ID  - 10_1007_s10587_013_0024_2
ER  - 
%0 Journal Article
%A Zhang, Zhen
%A Zhu, Xiaosheng
%A Yan, Xiaoguang
%T Totally reflexive modules with respect to a semidualizing bimodule
%J Czechoslovak Mathematical Journal
%D 2013
%P 385-402
%V 63
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0024-2/
%R 10.1007/s10587-013-0024-2
%G en
%F 10_1007_s10587_013_0024_2
Zhang, Zhen; Zhu, Xiaosheng; Yan, Xiaoguang. Totally reflexive modules with respect to a semidualizing bimodule. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 385-402. doi : 10.1007/s10587-013-0024-2. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0024-2/

Cité par Sources :