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Dec 21, 2011 at 11:33 comment added Graham Leuschke Actually, this is a terrible example. All these modules have finite projective dimension! I should have used $k[x]/(x^2)$; the residue field has infinite projective dimension and is not a direct limiit of modules of finite projective dimension.
Dec 21, 2011 at 10:53 vote accept User3568
Dec 20, 2011 at 16:25 history answered Graham Leuschke CC BY-SA 3.0