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.

In: Glasgow Mathematical Journal, Vol. 59, No. 3, 2017, p. 549-561.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Holm, HG 2017, 'The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings', Glasgow Mathematical Journal, vol. 59, no. 3, pp. 549-561. https://doi.org/10.1017/S0017089516000343

APA

Holm, H. G. (2017). The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings. Glasgow Mathematical Journal, 59(3), 549-561. https://doi.org/10.1017/S0017089516000343

Vancouver

Holm HG. The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings. Glasgow Mathematical Journal. 2017;59(3):549-561. https://doi.org/10.1017/S0017089516000343

Author

Holm, Henrik Granau. / The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings. In: Glasgow Mathematical Journal. 2017 ; Vol. 59, No. 3. pp. 549-561.

Bibtex

@article{86964f90b68e447bb6d2859df0ffac5e,
title = "The structure of balanced big Cohen-Macaulay modules over Cohen-Macaulay rings",
abstract = "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.",
author = "Holm, {Henrik Granau}",
year = "2017",
doi = "10.1017/S0017089516000343",
language = "English",
volume = "59",
pages = "549--561",
journal = "Glasgow Mathematical Journal",
issn = "0017-0895",
publisher = "Cambridge University Press",
number = "3",

}

RIS

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