Relative syzygies and grade of modules |
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Authors: | Zeng Feng Liu Zhao Yong Huang |
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Institution: | 1. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China
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Abstract: | Recently Takahashi established a new approximation theory for finitely generated modules over commutative Noetherian rings, which unifies the spherical approximation theorem due to Auslander and Bridger and the Cohen-Macaulay approximation theorem due to Auslander and Buchweitz. In this paper we generalize these results to much more general case over non-commutative rings. As an application, we establish a relation between the injective dimension of a generalized tilting module ω and the finitistic dimension with respect to ω. |
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