Geodesic
Rings on almost completely decomposable Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 5, pp. 93-101

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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. 
@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},
     publisher = {mathdoc},
     volume = {14},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_5_a5/}
}
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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/