On the dimension of an Abelian group
2021 (English)In: Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132, Vol. 27, no 4, p. 267-275Article in journal (Refereed) Published
Abstract [en]
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.
Place, publisher, year, edition, pages
Bulgarian Academy of Science , 2021. Vol. 27, no 4, p. 267-275
Keywords [en]
Abelian group, Dimension, Perpendicularity
National Category
Algebra and Logic
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:ltu:diva-88324DOI: 10.7546/nntdm.2021.27.4.267-275ISI: 000752399400026OAI: oai:DiVA.org:ltu-88324DiVA, id: diva2:1619401
Note
Validerad;2022;Nivå 2;2022-01-01 (johcin);
For correction, see: Tossavainen, T., & Haukkanen, P. (2022). Corrigendum to ‘On the dimension of an Abelian group’ [Notes on Number Theory and Discrete Mathematics, 2021, Volume 27, Number 4, Pages 267—275]. Notes on Number Theory and Discrete Mathematics, 28(1), 20–20. https://doi.org/10.7546/nntdm.2022.28.1.20
2021-12-132021-12-132022-03-14Bibliographically approved