The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings
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The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings. / Holm, Henrik Granau.
I: Glasgow Mathematical Journal, Bind 59, Nr. 3, 2017, s. 549-561.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings
AU - Holm, Henrik Granau
PY - 2017
Y1 - 2017
N2 - Over a Cohen–Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module, in the sense of Hochster, can be written as a direct limit of small CM modules. In analogy with Govorov and Lazard's characterization of flat modules as direct limits of finitely generated free modules, one can view this as a “structure theorem” for balanced big CM modules. (2) Every finitely generated module has a pre-envelope with respect to the class of finitely generated maximal CM modules. This result is, in some sense, dual to the existence of maximal CM approximations, which has been proved by Auslander and Buchweitz.
AB - Over a Cohen–Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module, in the sense of Hochster, can be written as a direct limit of small CM modules. In analogy with Govorov and Lazard's characterization of flat modules as direct limits of finitely generated free modules, one can view this as a “structure theorem” for balanced big CM modules. (2) Every finitely generated module has a pre-envelope with respect to the class of finitely generated maximal CM modules. This result is, in some sense, dual to the existence of maximal CM approximations, which has been proved by Auslander and Buchweitz.
U2 - 10.1017/S0017089516000343
DO - 10.1017/S0017089516000343
M3 - Journal article
AN - SCOPUS:84973557335
VL - 59
SP - 549
EP - 561
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
SN - 0017-0895
IS - 3
ER -
ID: 178888767