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Let R be a commutative Noetherian ring. We consider the question of when n-syzygy modules over R are n-torsionfree in the sense of Auslander and Bridger. Our tools include Serre’s condition and certain conditions on the local Gorenstein property of R. Our main result implies the converse of a celebrated theorem of Evans and Griffith.
This paper studies the relationship between Serre’s condition ( Rn ) and Auslander–Buchweitz’s maximal Cohen–Macaulay approximations. It is proved that a Gorenstein local ring satisfies ( Rn ) if and only if every maximal Cohen–Macaulay module is a direct summand of a maximal Cohen–Macaulay approximation of a (Cohen–Macaulay)...
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