Geodesic
Isomorphisms between endomorphism rings of projective modules
Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 353-355

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

Let R and S be arbitrary rings, RM and SN countably generated free modules, and let φ:End(RM)→End(sN) be an isomorphism between the endomorphism rings of M and N. Camillo [3] showed in 1984 that these assumptions imply that R and S are Morita equivalent rings. Indeed, as Bolla pointed out in [2], in this case the isomorphism φ must be induced by some Morita equivalence between R and S. The same holds true if one assumes that RM and SN are, more generally, non-finitely generated free modules. 
García, José Luis; Simón, Juan Jacobo. Isomorphisms between endomorphism rings of projective modules. Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 353-355. doi: 10.1017/S0017089500009939
@article{10_1017_S0017089500009939,
     author = {Garc{\'\i}a, Jos\'e Luis and Sim\'on, Juan Jacobo},
     title = {Isomorphisms between endomorphism rings of projective modules},
     journal = {Glasgow mathematical journal},
     pages = {353--355},
     year = {1993},
     volume = {35},
     number = {3},
     doi = {10.1017/S0017089500009939},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009939/}
}
TY  - JOUR
AU  - García, José Luis
AU  - Simón, Juan Jacobo
TI  - Isomorphisms between endomorphism rings of projective modules
JO  - Glasgow mathematical journal
PY  - 1993
SP  - 353
EP  - 355
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009939/
DO  - 10.1017/S0017089500009939
ID  - 10_1017_S0017089500009939
ER  - 
%0 Journal Article
%A García, José Luis
%A Simón, Juan Jacobo
%T Isomorphisms between endomorphism rings of projective modules
%J Glasgow mathematical journal
%D 1993
%P 353-355
%V 35
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009939/
%R 10.1017/S0017089500009939
%F 10_1017_S0017089500009939

[1] 1.Anderson, F. W. and Fuller, K. R., Rings and categories of modules. (Springer-Verlag, 1974). Google Scholar | DOI

[2] 2.Bolla, M., Isomorphisms between infinite matrix rings, Linear Algebra and Appl. 69 (1985), 239–247. Google Scholar | DOI

[3] 3.Camillo, V., Morita equivalence and infinite matrix rings, Proc. Amer. Math. Soc. 90 (1984), 186–188. Google Scholar | DOI

[4] 4.Franzsen, W. N. and Schultz, P., The endomorphism ring of a locally free module, J. Austral. Math. Soc. Ser. A 35 (1983), 308–326. Google Scholar | DOI

[5] 5.García, J. L., The characterization problem for endomorphism rings, J. Austral. Math. Soc. Ser. A 50 (1991), 116–137. Google Scholar | DOI

[6] 6.García, J. L. and Simón, J. J., Morita equivalence for idempotent rings, J. Pure Appl. Algebra 76 (1991), 39–56. Google Scholar | DOI

[7] 7.Rowen, L. H., Ring theory, Vol. 1 (Academic Press, 1988). Google Scholar

[8] 8.Wolfson, K. G., An ideal-theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358–386. Google Scholar | DOI

[9] 9.Bonami, L., Morita-equivalent rings are isomorphic, Arch. Math. 34 (1980), 108–110. Google Scholar | DOI

Cité par Sources :