Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Maximal perpendicularity in certain Abelian groups
Tampere University of Technology, Finland.
University of Tampere, Finland.
University of Tampere, Finland.
Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.ORCID iD: 0000-0002-7494-4632
2017 (English)In: Acta Universitatis Sapientiae, Mathematica, ISSN 2066-7752, Vol. 9, no 1, p. 235-247Article in journal (Refereed) Published
Abstract [en]

We define perpendicularity in an Abelian group G as a binary relation satisfying certain five axioms. Such a relation is maximal if it is not a subrelation of any other perpendicularity in G. A motivation for the study is that the poset (P, ⊆) of all perpendicularities in G is a lattice if G has a unique maximal perpendicularity, and only a meet-semilattice if not. We study the cardinality of the set of maximal perpendicularities and, on the other hand, conditions on the existence of a unique maximal perpendicularity in the following cases: G ≅ ℤn, G is finite, G is finitely generated, and G = ℤ ⊕ ℤ ⊕⋯. A few such conditions are found and a few conjectured. In studying ℝn, we encounter perpendicularity in a vector space.

Place, publisher, year, edition, pages
De Gruyter Open, 2017. Vol. 9, no 1, p. 235-247
Keywords [en]
Abelian group, perpendicularity
National Category
Discrete Mathematics Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:ltu:diva-65085DOI: 10.1515/ausm-2017-0016Scopus ID: 2-s2.0-85026624639OAI: oai:DiVA.org:ltu-65085DiVA, id: diva2:1131677
Note

Validerad; 2017; Nivå 2; 2017-08-15 (andbra)

Available from: 2017-08-15 Created: 2017-08-15 Last updated: 2017-11-24Bibliographically approved

Open Access in DiVA

fulltext(363 kB)11 downloads
File information
File name FULLTEXT01.pdfFile size 363 kBChecksum SHA-512
d6639a75915ca0e20f79a48d600a11a94e75a35be05b19affbfd68aa980c9d027a4f891ee8a30fe0de92b3e85b8bd08eac25f44b6771b572aefde42caf65396e
Type fulltextMimetype application/pdf

Other links

Publisher's full textScopushttps://www.degruyter.com/downloadpdf/j/ausm.2017.9.issue-1/ausm-2017-0016/ausm-2017-0016.pdf

Authority records BETA

Tossavainen, Timo

Search in DiVA

By author/editor
Tossavainen, Timo
By organisation
Education, Language, and Teaching
Discrete MathematicsDidactics

Search outside of DiVA

GoogleGoogle Scholar
Total: 11 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 98 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf