Displaying similar documents to “Estimates of global dimension”

Wakamatsu tilting modules with finite injective dimension

Guoqiang Zhao, Lirong Yin (2013)

Czechoslovak Mathematical Journal

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Let R be a left Noetherian ring, S a right Noetherian ring and R ω a Wakamatsu tilting module with S = End ( R ω ) . We introduce the notion of the ω -torsionfree dimension of finitely generated R -modules and give some criteria for computing it. For any n ≥ 0 , we prove that l . id R ( ω ) = r . id S ( ω ) ≤ n if and only if every finitely generated left R -module and every finitely generated right S -module have ω -torsionfree dimension at most n , if and only if every finitely generated left R -module (or right S -module) has generalized Gorenstein...

A generalization of the Auslander transpose and the generalized Gorenstein dimension

Yuxian Geng (2013)

Czechoslovak Mathematical Journal

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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...