Perpendicularity in an Abelian Group

Author:

Haukkanen Pentti1,Mattila Mika1,Merikoski Jorma K.1,Tossavainen Timo2

Affiliation:

1. School of Information Sciences, University of Tampere, 33014, Finland

2. School of Applied Educational Science and Teacher Education, University of Eastern Finland, P.O. Box 86, 57101 Savonlinna, Finland

Abstract

We give a set of axioms to establish a perpendicularity relation in an Abelian group and then study the existence of perpendicularities in(n,+)and(+,·)and in certain other groups. Our approach provides a justification for the use of the symboldenoting relative primeness in number theory and extends the domain of this convention to some degree. Related to that, we also consider parallelism from an axiomatic perspective.

Publisher

Hindawi Limited

Subject

Mathematics (miscellaneous)

Reference8 articles.

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Exploring Perpendicularity and Parallelism Through Play;Mathematics Magazine;2023-10-20

2. Maximal perpendicularity in certain Abelian groups;Acta Universitatis Sapientiae, Mathematica;2017-08-01

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