Geodesic
Rings on almost completely decomposable Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 93-101 
E. I. Kompantseva. Rings on almost completely decomposable Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 93-101. http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a5/
@article{FPM_2008_14_5_a5,
     author = {E. I. Kompantseva},
     title = {Rings on almost completely decomposable {Abelian} groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {93--101},
     year = {2008},
     volume = {14},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a5/}
}
TY  - JOUR
AU  - E. I. Kompantseva
TI  - Rings on almost completely decomposable Abelian groups
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2008
SP  - 93
EP  - 101
VL  - 14
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a5/
LA  - ru
ID  - FPM_2008_14_5_a5
ER  - 
%0 Journal Article
%A E. I. Kompantseva
%T Rings on almost completely decomposable Abelian groups
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 93-101
%V 14
%N 5
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a5/
%G ru
%F FPM_2008_14_5_a5

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

The absolute radical of an Abelian group $G$ is the intersection of radicals of all associative rings with additive group $G$. L. Fuchs formulated the problem on a description of absolute radicals of Abelian groups. For a group from some class of almost completely decomposable Abelian groups the absolute Jacobson radical is described. In the class of almost completely decomposable Abelian groups semisimple groups are described.

[1] Kompantseva E. I., “Poluprostye koltsa na vpolne razlozhimykh abelevykh gruppakh”, Fundament. i prikl. mat., 13:3 (2007), 69–80 | MR

[2] Beaumont R. A., Lawver D. A., “Strongly semisimple Abelian groups”, Pacific J. Math., 53:2 (1974), 327–336 | MR | Zbl

[3] Blagoveshchenskaya E., Mader A., “Decomposition of almost completely decomposable Abelian groups”, Abelian Group Theory and Related Topics. Conf. (August 1–7, 1993, Oberwolfach, Germany), Contemp. Math., 171, ed. R. Göbel, Amer. Math. Soc., Providence, 1994, 21–36 | MR | Zbl

[4] Fuchs L., Infinite Abelian Groups, Vols. 1, Academic Press, New York, 1970 ; Vol. 2, 1973 | MR | Zbl | MR

[5] Jacobson N., Structure of Rings, Amer. Math. Soc., Providence, 1956 | MR | Zbl

[6] Mader A., Almost Completely Decomposable Abelian Groups, Algebra, Logic, and Applications, 13, Gordon and Breach, Amsterdam, 1999