<abstract xmlns="http://www.w3.org/1999/xhtml"><p> A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases of associative and general rings). It is shown that for any such a group A, the quotient group modulo the square subgroup of A is a nil-group. Some results listed in [16] are generalized and corrected. Moreover, it is proved that for a given abelian group A, the square subgroup of A considered in the class of associative rings, is a characteristic subgroup of A.</p></abstract>

A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases of associative and general rings). It is shown that for any such a group A, the quotient group modulo the square subgroup of A is a nil-group. Some results listed in [16] are generalized and corrected. Moreover, it is proved that for a given abelian group A, the square subgroup of A considered in the class of associative rings, is a characteristic subgroup of A.

A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three

Annales Mathematicae Silesianae

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A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The...

A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three

Published Online: Aug 24, 2018

Page range: 319 - 331

Received: Oct 28, 2016

Accepted: Jun 01, 2017

DOI: https://doi.org/10.1515/amsil-2017-0009

Keywords
torsion-free abelian groups, associative rings, square subgroups, types

© 2018 Mateusz Woronowicz, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three

Published Online: Aug 24, 2018

Page range: 319 - 331

Received: Oct 28, 2016

Accepted: Jun 01, 2017

DOI: https://doi.org/10.1515/amsil-2017-0009

Keywordstorsion-free abelian groups, associative rings, square subgroups, types

© 2018 Mateusz Woronowicz, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
torsion-free abelian groups, associative rings, square subgroups, types