Article

On additive groups of associative and commutative rings

Published in: Quaestiones Mathematicae
Volume 40 , issue 4 , 2017 , pages: 527–537

DOI: 10.2989/16073606.2017.1302019

Author(s): R.R. Andruszkiewicz Institute of Mathematics, Poland , M. Woronowicz Institute of Mathematics, Poland

Keywords: Primary 20K99 , Secondary 13A15 , Primary 20K99 , Secondary 13A15

Abstract

The characterization of (A)CR-groups studied by Shalom Feigelstock [‘Additive groups of commutative rings’, Quaest. Math. 23 (2000), 241–245] is complemented. In particular, the theorem characterizing mixed ACR-groups is proved and numerous new examples of (A)CR-group are given. Abelian groups A such that any ring with the additive group A is associative and commutative are partially described. Some new results for torsion-free and mixed TI-groups are obtained.

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