Complete intersection dimensions and Foxby classes |
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Authors: | Sean Sather-Wagstaff |
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Institution: | Department of Mathematics, 300 Minard Hall, North Dakota State University, Fargo, ND 58105-5075, USA |
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Abstract: | Let R be a local ring and M a finitely generated R-module. The complete intersection dimension of M-defined by Avramov, Gasharov and Peeva, and denoted -is a homological invariant whose finiteness implies that M is similar to a module over a complete intersection. It is related to the classical projective dimension and to Auslander and Bridger’s Gorenstein dimension by the inequalities .Using Blanco and Majadas’ version of complete intersection dimension for local ring homomorphisms, we prove the following generalization of a theorem of Avramov and Foxby: Given local ring homomorphisms φ:R→S and ψ:S→T such that φ has finite Gorenstein dimension, if ψ has finite complete intersection dimension, then the composition ψ°φ has finite Gorenstein dimension. This follows from our result stating that, if M has finite complete intersection dimension, then M is C-reflexive and is in the Auslander class AC(R) for each semidualizing R-complex C. |
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Keywords: | 13A35 13B10 13C05 13D05 13D07 13D25 14B25 |
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