<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Almost complete description of abelian groups (<italic>A</italic>, +, 0) such that every associative ring <italic>R</italic> with the additive group <italic>A</italic> satisfies the condition: every subgroup of <italic>A</italic> is an ideal of <italic>R</italic>, is given. Some new results for <italic>SR</italic>-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 <italic>nil</italic>-groups is complemented using only elementary methods.</p></abstract>

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.

A Note on Additive Groups of Some Specific Associative Rings

Institute of Mathematics, University of Białystok, Ciołkowskiego 1M, 15-267 Białystok,

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A Note on Additive Groups of Some Specific Associative Rings"}

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 Note on Additive Groups of Some Specific Associative Rings

Published Online: Sep 23, 2016

Page range: 219 - 229

Received: Mar 04, 2015

Accepted: Oct 07, 2015

DOI: https://doi.org/10.1515/amsil-2015-0013

Keywords
-groups, ideals, associative rings

© 2016 Mateusz Woronowicz, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Note on Additive Groups of Some Specific Associative Rings

Published Online: Sep 23, 2016

Page range: 219 - 229

Received: Mar 04, 2015

Accepted: Oct 07, 2015

DOI: https://doi.org/10.1515/amsil-2015-0013

Keywords-groups, ideals, associative rings

© 2016 Mateusz Woronowicz, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
-groups, ideals, associative rings