Geodesic
Radicals of endomorphism rings of torsion-free Abelian groups
Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 209-222 
P. A. Krylov. Radicals of endomorphism rings of torsion-free Abelian groups. Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 209-222. http://geodesic.mathdoc.fr/item/SM_1974_24_2_a1/
@article{SM_1974_24_2_a1,
     author = {P. A. Krylov},
     title = {Radicals of endomorphism rings of torsion-free {Abelian} groups},
     journal = {Sbornik. Mathematics},
     pages = {209--222},
     year = {1974},
     volume = {24},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_24_2_a1/}
}
TY  - JOUR
AU  - P. A. Krylov
TI  - Radicals of endomorphism rings of torsion-free Abelian groups
JO  - Sbornik. Mathematics
PY  - 1974
SP  - 209
EP  - 222
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1974_24_2_a1/
LA  - en
ID  - SM_1974_24_2_a1
ER  - 
%0 Journal Article
%A P. A. Krylov
%T Radicals of endomorphism rings of torsion-free Abelian groups
%J Sbornik. Mathematics
%D 1974
%P 209-222
%V 24
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1974_24_2_a1/
%G en
%F SM_1974_24_2_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with questions related to the nil radical and the Jacobson radical of the endomorphism rings of torsion-free Abelian groups. The most complete results are obtained for groups of finite rank. A characterization is given for the Jacobson radical of the endomorphism ring of a torsion-free Abelian group of finite rank. The question of when the Jacobson radical of the endomorphism ring of a torsion-free Abelian group of finite rank is nilpotent (equal to zero) is completely settled. Bibliography: 7 titles.

[1] J. D. Reid, “On the ring of quasi-endomorphisms of a torsion-free group”, Topics in abelian groups, Chicago, 1963, 51–68 | MR

[2] R. A. Beaumont, R. S. Pierce, Torsion-free groups of rank two, Mem. Amer. Math. Soc., 38, Providence, 1961, 41 | MR | Zbl

[3] A. L. S. Corner, “Endomorphism ring of torsion-free abelian groups”, Proc. internat. Conf. Theory of Groups, Canberra, 1967, 59–69 | Zbl

[4] I. Lambek, Koltsa i moduli, izd-vo «Mir», Moskva, 1971 | MR

[5] L. Fuchs, Infinite abelian groups, vol. 1, Academic Press, New York–London, 1970 | MR | Zbl

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

[7] L. Fuchs, “Recent results and problems on abelian groups”, Topics in abelian groups, Chicago, 1963, 9–40 | MR