Krapež, Aleksandar Quadratic level quasigroup equations with four variables. II: The lattice of varieties. (English) Zbl 1299.20093 Publ. Inst. Math., Nouv. Sér. 93(107), 29-47 (2013). 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)]. Cited in 1 Document MSC: 20N05 Loops, quasigroups 08B15 Lattices of varieties 39B52 Functional equations for functions with more general domains and/or ranges Keywords:quasigroup functional equations; quasigroup identities; quasigroup varieties; lattices of varieties Citations:Zbl 1229.39035 PDFBibTeX XMLCite \textit{A. Krapež}, Publ. Inst. Math., Nouv. Sér. 93(107), 29--47 (2013; Zbl 1299.20093) Full Text: DOI