A note on additive groups of some specific associative rings

Mateusz Woronowicz

Published: 2016-09-23

Vol. 30 (2016)

A note on additive groups of some specific associative rings

Mateusz Woronowicz

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

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Woronowicz, M. (2016). A note on additive groups of some specific associative rings. Annales Mathematicae Silesianae, 30, 219–229. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13966

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Vol. 30 (2016)
Published: 2016-09-23

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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