Geodesic
A Remark on Colimits
Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 496-499

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

Let MR be a right module over the associative ring R (with 1). Assume one has an expression for M as a colimit (direct limit) of a system over the (directed) poset D. A natural way to get M as a colimit of the family {F∞ —” Fβ|∞, fβ ∈ E} for some subset £ of D is to take E cofinal in D. However, if one is concerned about the cardinality of the set E, cofinal subsets may be too large. Let us look at a specific example. Lazard [3] has shown that any flat MR is a direct limit of finitely generated free R-modules. The cardinality of his indexing set depends on the cardinality of M. 
Osofsky, Barbara L. A Remark on Colimits. Canadian journal of mathematics, Tome 27 (1975) no. 3, pp. 496-499. doi: 10.4153/CJM-1975-060-5
@article{10_4153_CJM_1975_060_5,
     author = {Osofsky, Barbara L.},
     title = {A {Remark} on {Colimits}},
     journal = {Canadian journal of mathematics},
     pages = {496--499},
     year = {1975},
     volume = {27},
     number = {3},
     doi = {10.4153/CJM-1975-060-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-060-5/}
}
TY  - JOUR
AU  - Osofsky, Barbara L.
TI  - A Remark on Colimits
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 496
EP  - 499
VL  - 27
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-060-5/
DO  - 10.4153/CJM-1975-060-5
ID  - 10_4153_CJM_1975_060_5
ER  - 
%0 Journal Article
%A Osofsky, Barbara L.
%T A Remark on Colimits
%J Canadian journal of mathematics
%D 1975
%P 496-499
%V 27
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-060-5/
%R 10.4153/CJM-1975-060-5
%F 10_4153_CJM_1975_060_5

[1] 1. Kaplansky, I., Projective modules, Ann. of Math. 68 (1958), 372–377. Google Scholar

[2] 2. Kaplansky, I., Fields and rings (University of Chicago Press, Chicago, 1969). Google Scholar

[3] 3. Lazard, D., Sur les modules plats, C. R. Acad Sci. Paris 258 (1964), 6313–6316. Google Scholar

[4] 4. Osofsky, B., Upper bounds on homologuai dimensions, Nagoya Math. J. 32 (1968), 315–322. Google Scholar

[5] 5. Osofsky, B., Homological dimensions of modules, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, Number 12 (American Math. Soc, Providence, Google Scholar

[6] 6. Eilenberg, S. and Steenrod, N., Foundations of algebraic topology (Princeton University Press, Princeton, 1952). Google Scholar

Cité par Sources :