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A generalization of the Auslander transpose and the generalized Gorenstein dimension
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 143-156
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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 
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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

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