On Birkhoff's quasigroup axioms

Autor: D.I. Pushkashu, V. A. Shcherbacov, J. D. Phillips, A.V. Shcherbacov
Rok vydání: 2016
Předmět:
Zdroj: Journal of Algebra. 457:7-17
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2016.02.024
Popis: Birkhoff defined a quasigroup as an algebra ( Q , ⋅ , \ , / ) that satisfies the following six identities: x ⋅ ( x \ y ) = y , ( y / x ) ⋅ x = y , x \ ( x ⋅ y ) = y , ( y ⋅ x ) / x = y , x / ( y \ x ) = y , and ( x / y ) \ x = y . We investigate triples and tetrads of identities composed of these six, emphasizing those that axiomatize the variety of quasigroups.
Databáze: OpenAIRE
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