Equations which preserve the height of variables

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...

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Bibliographic Details
Published inAequationes mathematicae Vol. 70; no. 1-2; pp. 63 - 76
Main Authors g-Rob, Wolfgang, Krapez, Aleksandar
Format Journal Article
LanguageEnglish
Published Basel Springer Nature B.V 01.09.2005
Subjects
Linear equations
Mathematical analysis
Mathematical functions
Preserves
Preserving
Proof theory
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Summary: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 formulas of a general solution are also given. Some results of Belousov are discussed and partially generalized.[PUBLICATION ABSTRACT]
Bibliography:ObjectType-Article-1
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ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-005-2790-x