Open AccessQuadratic level quasigroup equations with four variables I
Author(s) -
Aleksandar Krapež
Publication year - 2007
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim0795053k
Subject(s) - quasigroup , mathematics , equivalence (formal languages) , quadratic equation , equivalence class (music) , class (philosophy) , nonlinear system , pure mathematics , algebra over a field , computer science , physics , geometry , quantum mechanics , artificial intelligence
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} (1 _< 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 recent papers of F?rg-Rob and Krapez, and Polonijo.