Equations which preserve the height of variables

• Published in: Aequationes mathematicae Vol. 70; no. 1-2; pp. 63 - 76
• Main Authors: g-Rob, Wolfgang, Krapez, Aleksandar
• Format: Journal Article
• Language: English
• Published: Basel Springer Nature B.V 01.09.2005
• Subjects: Linear equations; Mathematical analysis; Mathematical functions; Preserves; Preserving; Proof theory

We define a special class of linear quasigroup functional equations and call them height preserving equations (short for the equations which preserve the height of variables). It is proved that a quasigroup satisfying a height preserving but not Belousov equation is isotopic to an abelian group. The...