Authors: Krapež, Aleksandar 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Quadratic level quasigroup equations with four variables I
Journal: Publications de l'Institut Mathematique
Issue: 95
First page: 53
Last page: 67
Issue Date: 1-Jan-2007
ISSN: 0350-1302
DOI: 10.2298/PIM0795053K
We consider a class of functional equations with one operational symbol which is assumed to be a quasigroup. Equations are quadratic, level and have four variables each. Therefore, they are of the form x1x2 · x3x4 = x5x6 · x7x8 with xi ∈ {x, y, u, v} (I ≤ i ≤ 8) with each of the variables occurring exactly twice in the equation. There are 105 such equations. They separate into 19 equivalence classes defining 19 quasigroup varieties. The paper (partially) generalizes the results of some retent papers of Förg-Rob and Krapeẑ, and Polonijo.
Keywords: Balanced equation | Belousov equation | Functional equation | Gemini equation | General solution | Isotopy | Level equation | Medial equation | Quadratic equation | Quasigroup | Quasigroup (left, right) linear over a group | T-quasigroup | Variety
Publisher: Mathematical Institute of the SASA
Project: Ministry of Sciences of Serbia, Grants 144013 and 144018

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