2014/10/21 by Henrik Holm, Holm, Henrik
Mathematics · #13C14 #13D05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C14 #msc:13D05
paper · pdf · doi:10.48550/arxiv.1410.5611
11 pages
arxiv created 2014/10/21 · arxiv updated 2014/10/22
Auslander and Buchweitz have proved that every finitely generated module over a Cohen-Macaulay (CM) ring with a dualizing module admits a so-called maximal CM approximation. In terms of relative homological algebra, this means that every finitely generated module has a special maximal CM precover. In this paper, we prove the existence of special maximal CM preenvelopes and, in the case where the ground ring is henselian, of maximal CM envelopes. We also characterize the rings over which every finitely generated module has a maximal CM envelope with the unique lifting property. Finally, we show that cosyzygies with respect to the class of maximal CM modules must eventually be maximal CM, and we compute some examples.