an:06165375
Zbl 1264.51012
Haukkanen, Pentti; Mattila, Mika; Merikoski, Jorma K.; Tossavainen, Timo
Perpendicularity in an Abelian group
EN
Int. J. Math. Math. Sci. 2013, Article ID 983607, 8 p. (2013).
00315088
2013
j
51M05 51F20 20K01
Summary: We give a set of axioms to establish a perpendicularity relation in an abelian group and then study the existence of perpendicularities in \((\mathbb Z_n, +)\) and \((\mathbb Q_+, \cdot)\) and in certain other groups. Our approach provides a justification for the use of the symbol \(\perp\) denoting 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.