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/