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Annales Mathematicae Silesianae

Editor-in-Chief: Sablik, Maciej

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Mathematical Citation Quotient (MCQ) 2016: 0.10

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A Note on Additive Groups of Some Specific Associative Rings

Mateusz Woronowicz
Published Online: 2016-09-23 | DOI: https://doi.org/10.1515/amsil-2015-0013

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.

Keywords: nil-groups; ideals; associative rings

MSC 2010: 20K99

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About the article

Received: 2015-03-04

Revised: 2015-10-05

Accepted: 2015-10-07

Published Online: 2016-09-23

Published in Print: 2016-09-01


Citation Information: Annales Mathematicae Silesianae, Volume 30, Issue 1, Pages 219–229, ISSN (Online) 0860-2107, DOI: https://doi.org/10.1515/amsil-2015-0013.

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© 2016 Mateusz Woronowicz, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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