Almost complete description of abelian groups (A, +, 0) such that every associative ring R with the additive group A satisfies the condition: every subgroup of A is an ideal of R, is given. Some new results for SR-groups in the case of associative rings are also achieved. The characterization of abelian torsion-free groups of rank one and their direct sums which are not nil-groups is complemented using only elementary methods.
@article{bwmeta1.element.doi-10_1515_amsil-2015-0013, author = {Mateusz Woronowicz}, title = {A Note on Additive Groups of Some Specific Associative Rings}, journal = {Annales Mathematicae Silesianae}, volume = {30}, year = {2016}, pages = {219-229}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0013} }
Mateusz Woronowicz. A Note on Additive Groups of Some Specific Associative Rings. Annales Mathematicae Silesianae, Tome 30 (2016) pp. 219-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0013/