Endomorphism rings of free modules over perfect rings
Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 138-147 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We find a condition on the endomorphism rings of free right $R$-modules which is equivalent to $R$ being a right perfect ring. We also obtain different characterizations of right perfect rings with nonzero right annihilators of the proper left ideals of finite descent. Bibliography: 15 titles.
@article{SM_1972_17_1_a6,
     author = {G. M. Brodskii},
     title = {Endomorphism rings of free modules over perfect rings},
     journal = {Sbornik. Mathematics},
     pages = {138--147},
     year = {1972},
     volume = {17},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_17_1_a6/}
}
TY  - JOUR
AU  - G. M. Brodskii
TI  - Endomorphism rings of free modules over perfect rings
JO  - Sbornik. Mathematics
PY  - 1972
SP  - 138
EP  - 147
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1972_17_1_a6/
LA  - en
ID  - SM_1972_17_1_a6
ER  - 
%0 Journal Article
%A G. M. Brodskii
%T Endomorphism rings of free modules over perfect rings
%J Sbornik. Mathematics
%D 1972
%P 138-147
%V 17
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1972_17_1_a6/
%G en
%F SM_1972_17_1_a6
G. M. Brodskii. Endomorphism rings of free modules over perfect rings. Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 138-147. http://geodesic.mathdoc.fr/item/SM_1972_17_1_a6/

[1] H. Bass, “Finitistic dimension and a homological generalization of semi-primary rings”, Trans. Amer. Math. Soc., 95:3 (1960), 466–488 | DOI | MR | Zbl

[2] G. M. Tsukerman, “Koltsa endomorfizmov svobodnykh modulei”, Sib. matem. zh., 7:5 (1966), 1161–1167 | Zbl

[3] N. Dzhekobson, Stroenie kolets, IL, Moskva, 1961

[4] L. A. Skornyakov, Elementy teorii struktur, Nauka, Moskva, 1970 | MR

[5] H. Lenzing, “Uber koharente Ringe”, Math. Z., 114:3 (1970), 201–212 | DOI | MR | Zbl

[6] E. M. Patterson, “On the radicals of rings of row-finite matrices”, Proc. Roy. Soc. Edinburgh, A66:1 (1961–1962), 42–46 | MR

[7] P. M. Cohn, Morita-equivalence and duality, Math. Notes, Queen Mary College, London, 1968 | MR

[8] A. Kartan, S. Eilenberg, Gomologicheskaya algebra, IL, Moskva, 1960

[9] B. S. Chwe, J. Neggers, “On the extension of linearly independent subsets of free modules to bases”, Proc. Amer. Math. Soc., 24:3 (1970), 466–470 | DOI | MR | Zbl

[10] I. Kaplanskii, “Proektivnye moduli”, Matematika, 4:1 (1960), 3–8

[11] V. E. Govorov, “Koltsa, nad kotorymi ploskie moduli yavlyayutsya svobodnymi”, DAN SSSR, 144:5 (1962), 965–967 | MR | Zbl

[12] R. Ber, Lineinaya algebra i proektivnaya geometriya, IL, Moskva, 1955

[13] G. M. Tsukerman, “O treugolnoi teorii Galua”, Sib. matem. zh., 4:5 (1963), 1194–1197 | Zbl

[14] G. M. Brodskii, “Shteinitsevy moduli”, Matem. issledovaniya, VII:2(24) (1972), 14–28 | MR

[15] B. S. Chwe, J. Neggers, “Rings classified by properties of modules”, Notices Amer. Math. Soc., 18:1 (1971), 120