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Article

Aghdam, A. M. ; Karimi, F. ; Najafizadeh, A.
On the subgroups of completely decomposable torsion-free groups that are ideals in every ring. (English). Archivum Mathematicum, vol. 48 (2012), issue 2, pp. 107-112
MSC: 20K15 | MR 2946210 | DOI: 10.5817/AM2012-2-107
Keywords:
completely decomposable group; type; ring
Summary:
In this paper we consider completely decomposable torsion-free groups and we determine the subgroups which are ideals in every ring over such groups.
References:
[1] Aghdam, A. M., Najafizadeh, A.: Square subgroups of rank two abelian groups. Colloq. Math. 117 (1) (2009), 19–28. DOI 10.4064/cm117-1-2 | MR 2539546 | Zbl 1186.20037
[2] Fried, E.: On the subgroups of an abelian group that are ideals in every ring. Proc. Colloq. Abelian groups, Budapest, 1964, pp. 51–55. MR 0168670 | Zbl 0135.05901
[3] Fuchs, L.: Infinite abelian groups. Academic Press, New York–London, 1973. MR 0349869 | Zbl 0257.20035
[4] Najafizadeh, A., Aghdam, A. M., Karimi, F.: On the ideals of torsion–free rings of rank one and two. Math. Notes (to appear).
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