Timo Tossavainen and Pentti Haukkanen
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 267–275
DOI: 10.7546/nntdm.2021.27.4.267-275
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Authors and affiliations
Timo Tossavainen
Department of Health, Education and Technology, Lulea University of Technology
SE-97187 Lulea, Sweden
Pentti Haukkanen
Faculty of Information Technology and Communication Sciences, Tampere University
FI-33014 Tampere University, Finland
Abstract
We introduce a measure of dimensionality of an Abelian group. Our definition of dimension is based on studying perpendicularity relations in an Abelian group. For G ≅ ℤn, dimension and rank coincide but in general they are different. For example, we show that dimension is sensitive to the overall dimensional structure of a finite or finitely generated Abelian group, whereas rank ignores the torsion subgroup completely.
Keywords
- Abelian group
- Dimension
- Perpendicularity
2020 Mathematics Subject Classification
- 11A41
- 20K25
- 52C99
References
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Corrigendum
- Tossavainen, T., & Haukkanen, P. (2022). Corrigendum to “On the dimension of an Abelian group” [Notes on Number Theory and Discrete Mathematics, 2022, Volume 27, Number 4, Pages 267–275]. Notes on Number Theory and Discrete Mathematics, 28(1), 20.
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Cite this paper
Tossavainen, T., & Haukkanen, P. (2021). On the dimension of an Abelian group. Notes on Number Theory and Discrete Mathematics, 27(4), 267-275, DOI: 10.7546/nntdm.2021.27.4.267-275.