A note on the square subgroups of decomposable torsion-free abelian groups of rank three
Journal Title: Annales Mathematicae Silesianae - Year 2018, Vol 32, Issue
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.
Authors and Affiliations
Mateusz Woronowicz
Keywords
Related Articles
- EP ID EP525032
- DOI 10.1515/amsil-2017-0009
- Views 103
- Downloads 0
On the continuous dependence of solutions to orthogonal additivity problem on given functions
We show that the solution to the orthogonal additivity problem in real inner product spaces depends continuously on the given function and provide an application of this fact.
Complementary results to Heuvers’s characterization of logarithmic functions
Based on a characterization of logarithmic functions due to Heuvers we develop analogous results for multiplicative, exponential and additive functions, respectively.
Communication complexity and linearly ordered sets
The paper is devoted to the communication complexity of lattice operations in linearly ordered finite sets. All well known techniques ([4, Chapter 1]) to determine the communication complexity of the infimum function in...
Characterizations of rotundity and smoothness by approximate orthogonalities
In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we provide some new characterizations of rotundity and smoothness of...
Generalizations of some integral inequalities for fractional integrals
In this paper we give generalizations of the Hadamard-type inequalities for fractional integrals. As special cases we derive several Hadamard type inequalities.