Geodesic
A generalization of the Auslander transpose and the generalized Gorenstein dimension
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 143-156 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.1007/s10587-013-0009-1
Classification : 13C15, 13E05, 16E10, 16P40
Keywords: transpose; semidualizing module; generalized Gorenstein dimension; depth; Auslander-Bridger formula 
@article{10_1007_s10587_013_0009_1,
     author = {Geng, Yuxian},
     title = {A generalization of the {Auslander} transpose and the generalized {Gorenstein} dimension},
     journal = {Czechoslovak Mathematical Journal},
     pages = {143--156},
     year = {2013},
     volume = {63},
     number = {1},
     doi = {10.1007/s10587-013-0009-1},
     mrnumber = {3035502},
     zbl = {1274.13022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0009-1/}
}
TY  - JOUR
AU  - Geng, Yuxian
TI  - A generalization of the Auslander transpose and the generalized Gorenstein dimension
JO  - Czechoslovak Mathematical Journal
PY  - 2013
SP  - 143
EP  - 156
VL  - 63
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0009-1/
DO  - 10.1007/s10587-013-0009-1
LA  - en
ID  - 10_1007_s10587_013_0009_1
ER  - 
%0 Journal Article
%A Geng, Yuxian
%T A generalization of the Auslander transpose and the generalized Gorenstein dimension
%J Czechoslovak Mathematical Journal
%D 2013
%P 143-156
%V 63
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0009-1/
%R 10.1007/s10587-013-0009-1
%G en
%F 10_1007_s10587_013_0009_1
Geng, Yuxian. A generalization of the Auslander transpose and the generalized Gorenstein dimension. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 143-156. doi: 10.1007/s10587-013-0009-1

Cité par Sources :