| Authors: | Krapež, Aleksandar | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Quadratic level quasigroup equations with four variables II: The lattice of varieties | Journal: | Publications de l'Institut Mathematique | Volume: | 93 | Issue: | 107 | First page: | 29 | Last page: | 47 | Issue Date: | 26-Jul-2013 | Rank: | M23 | ISSN: | 0350-1302 | DOI: | 10.2298/PIM1307029K | Abstract: | We consider a class of quasigroup identities (with one operation symbol) of the form x1x2.x3x4 = x5x6.x7x8 and with xi Ε {x, y, u, v} (1 ≤ i ≤ 8) with each of x, y, u, v occurring exactly twice in the identity. There are 105 such identities. They generate 26 quasigroup varieties. The lattice of these varieties is given. |
Keywords: | Lattice of varieties | Quadratic level quasigroup equation | Quasigroup | Quasigroup functional equation | Quasigroup identity | Quasigroup variety | Publisher: | Mathematical Institute of the SASA | Project: | Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security Representations of logical structures and formal languages and their application in computing |
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