Geodesic
THE STRUCTURE OF BALANCED BIG COHEN–MACAULAY MODULES OVER COHEN–MACAULAY RINGS
Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 549-561

Voir la notice de l'article provenant de la source Cambridge

DOI

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. 
HOLM, HENRIK. THE STRUCTURE OF BALANCED BIG COHEN–MACAULAY MODULES OVER COHEN–MACAULAY RINGS. Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 549-561. doi: 10.1017/S0017089516000343
@article{10_1017_S0017089516000343,
     author = {HOLM, HENRIK},
     title = {THE {STRUCTURE} {OF} {BALANCED} {BIG} {COHEN{\textendash}MACAULAY} {MODULES} {OVER} {COHEN{\textendash}MACAULAY} {RINGS}},
     journal = {Glasgow mathematical journal},
     pages = {549--561},
     year = {2017},
     volume = {59},
     number = {3},
     doi = {10.1017/S0017089516000343},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000343/}
}
TY  - JOUR
AU  - HOLM, HENRIK
TI  - THE STRUCTURE OF BALANCED BIG COHEN–MACAULAY MODULES OVER COHEN–MACAULAY RINGS
JO  - Glasgow mathematical journal
PY  - 2017
SP  - 549
EP  - 561
VL  - 59
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000343/
DO  - 10.1017/S0017089516000343
ID  - 10_1017_S0017089516000343
ER  - 
%0 Journal Article
%A HOLM, HENRIK
%T THE STRUCTURE OF BALANCED BIG COHEN–MACAULAY MODULES OVER COHEN–MACAULAY RINGS
%J Glasgow mathematical journal
%D 2017
%P 549-561
%V 59
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000343/
%R 10.1017/S0017089516000343
%F 10_1017_S0017089516000343

Cité par Sources :