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Quadratic level quasigroup equations with four variables. II: The lattice of varieties. (English) Zbl 1299.20093

Summary: We consider a class of quasigroup identities (with one operation symbol) of the form \(x_1x_2\cdot x_3x_4=x_5x_6\cdot x_7x_8\) and with \(x_i\in\{x,y,u,v\}\) (\(1\leq i\leq 8\)) with each of the variables occurring exactly twice in the identity. There are 105 such identities. They generate 26 quasigroup varieties. The lattice of these varieties is given.
For part I see A. Krapež [Publ. Inst. Math., Nouv. Sér. 81(95), 53-67 (2007; Zbl 1229.39035)].

MSC:

20N05 Loops, quasigroups
08B15 Lattices of varieties
39B52 Functional equations for functions with more general domains and/or ranges

Citations:

Zbl 1229.39035
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