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

QUADRATIC LEVEL QUASIGROUP EQUATIONS WITH FOUR VARIABLES II: THE LATTICE OF VARIETIESAleksandar KrapezMathematical Institute SASA, Kneza Mihaila 36, Belgrade, SerbiaAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
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
