The Jacobson radical of the endomorphism ring for an Abelian group. (Russian, English) Zbl 1065.20066
Algebra Logika 43, No. 1, 60-76 (2004); translation in Algebra Logic 43, No. 1, 34-43 (2004).
The author finds the Jacobson radical of the endomorphism ring for an almost decomposable Abelian torsion-free group. An analogous problem was solved earlier for the groups of finite rank by A. Mader and P. Schultz [in Commun. Algebra 28, No. 1, 51-68 (2000; Zbl 0952.20043)]. The Jacobson radical of the endomorphism ring is also computed for self-small mixed Abelian sp-groups \(G\) such that \(G/T(G)\) has finite rank.
Reviewer: A. P. Pozhidaev (Novosibirsk)
MSC:
| 20K30 | Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups |
| 20K20 | Torsion-free groups, infinite rank |
| 20K15 | Torsion-free groups, finite rank |
| 16S50 | Endomorphism rings; matrix rings |
| 16N20 | Jacobson radical, quasimultiplication |
