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A generalization of the Auslander transpose and the generalized Gorenstein dimension

Yuxian Geng — 2013

Czechoslovak Mathematical Journal

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...

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