A generalization of the Auslander transpose and the generalized Gorenstein dimension

作者：Geng, Yuxian^*

来源：Czechoslovak Mathematical Journal, 2013, 63(1): 143-156.

DOI：10.1007/s10587-013-0009-1

• transpose
• semidualizing module
• generalized Gorenstein dimension
• depth
• Auslander-Bridger formula

Let R be a left and right Noetherian ring and C a semidualizing R-bimodule. We introduce a transpose 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 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.

• 出版日期2013-3
• 单位江苏大学