A note on the square subgroups of decomposable torsion-free abelian groups of rank three

Mateusz Woronowicz

Published: 2017-10-04

Vol. 32 (2018)

A note on the square subgroups of decomposable torsion-free abelian groups of rank three

Mateusz Woronowicz

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.

Keywords:

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

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Woronowicz, M. (2017). A note on the square subgroups of decomposable torsion-free abelian groups of rank three. Annales Mathematicae Silesianae, 32, 319–331. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13930

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Vol. 32 (2018)
Published: 2018-08-24

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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