Smith, Jonathan D. H. Axiomatization of quasigroups. (English) Zbl 1135.20048 Discuss. Math., Gen. Algebra Appl. 27, No. 1, 21-33 (2007). In this paper the author presents a new definition of quasigroups, using heterogeneous algebras known as hyperquasigroups. With this new definition, just two identities are needed: hypercommutativity and hypercancellativity. Reviewer: C. Pereira da Silva (Curitiba) Cited in 1 Document MSC: 20N05 Loops, quasigroups 08A68 Heterogeneous algebras 20A05 Axiomatics and elementary properties of groups 20N20 Hypergroups Keywords:quasigroups; heterogeneous algebras; hyperidentities; hyperquasigroups; identities; hypercommutativity; hypercancellativity; axioms PDFBibTeX XMLCite \textit{J. D. H. Smith}, Discuss. Math., Gen. Algebra Appl. 27, No. 1, 21--33 (2007; Zbl 1135.20048) Full Text: DOI