Symmetric linear operator identities in quasigroups
Reza Akhtar (2017)
Commentationes Mathematicae Universitatis Carolinae
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Let be a quasigroup. Associativity of the operation on can be expressed by the symbolic identity of left and right multiplication maps; likewise, commutativity can be expressed by the identity . In this article, we investigate symmetric linear identities: these are identities in left and right multiplication symbols in which every indeterminate appears exactly once on each side, and whose sides are mirror images of each other. We determine precisely which identities imply associativity...