کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4589181 | 1334212 | 2006 | 12 صفحه PDF | دانلود رایگان |
Let Λ be a right quasi k-Gorenstein ring. For each dth syzygy module M in modΛ (where 0⩽d⩽k−1), we obtain an exact sequence 0→B→M⊕P→C→0 in modΛ with the properties that it is dual exact, P is projective, C is a (d+1)st syzygy module, B is a dth syzygy of and the right projective dimension of B∗ is less than or equal to d−1. We then give some applications of such an exact sequence as follows. (1) We obtain a chain of epimorphisms concerning M, and by dualizing it we then get the spherical filtration of Auslander and Bridger for M∗. (2) We get Auslander and Bridger's Approximation Theorem for each reflexive module in modΛop. (3) We show that for any 0⩽d⩽k−1 each dth syzygy module in modΛ has an Evans–Griffith presentation. As an immediate consequence of (3), we have that, if Λ is a commutative Noetherian ring with finite self-injective dimension, then for any non-negative integer d, each dth syzygy module in modΛ has an Evans–Griffith presentation, which generalizes an Evans and Griffith's result to much more general setting.
Journal: Journal of Algebra - Volume 299, Issue 1, 1 May 2006, Pages 21-32