EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 93(107), pp. 29–47 (2013)

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QUADRATIC LEVEL QUASIGROUP EQUATIONS WITH FOUR VARIABLES II: THE LATTICE OF VARIETIES

Aleksandar Krapez

Mathematical Institute SASA, Kneza Mihaila 36, Belgrade, Serbia

Abstract: 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 $x_i\in\{x,y,u,v\}$ ($1\leq i\leq8)$ 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.

Keywords: quasigroup, quasigroup functional equation, quadratic level quasigroup equation, quasigroup identity, quasigroup variety, lattice of varieties

Classification (MSC2000): 20N05; 08B15, 39B52

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Electronic fulltext finalized on: 2 Apr 2013. This page was last modified: 8 Apr 2013.

© 2013 Mathematical Institute of the Serbian Academy of Science and Arts
© 2013 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition