Maximal perpendicularity in certain Abelian groups-Reference-Cited by-同舟云学术

Maximal perpendicularity in certain Abelian groups

Published:2017-08-01 Issue:1 Volume:9 Page:235-247
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Mattila Mika¹,Merikoski Jorma K.²,Haukkanen Pentti²,Tossavainen Timo³

Affiliation:

1. Department of Mathematics , Tampere University of Technology , Finland

2. School of Information Sciences , University of Tampere , Finland

3. Department of Art, Communication and Education , Lulea University of Technology , Sweden

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference7 articles.

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