Axiomatization of quasigroups

• Autorzy: Jonathan D.H. Smith
• Języki publikacji: EN

Abstrakty

EN

Quasigroups were originally described combinatorially, in terms of existence and uniqueness conditions on the solutions to certain equations. Evans introduced a universal-algebraic characterization, as algebras with three binary operations satisfying four identities. Now, quasigroups are redefined as heterogeneous algebras, satisfying just two conditions respectively known as hypercommutativity and hypercancellativity.

Słowa kluczowe

EN

quasigroup; heterogeneous algebra; hyperidentity

Kategorie tematyczne

• 20N05: Loops, quasigroups
• 08A68: Heterogeneous algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2007
• Tom: 27
• Numer: 1

Daty

wydano

2006

otrzymano

2006-02-27

poprawiono

2006-03-31

Twórcy

autor

Jonathan D.H. Smith

• Department of Mathematics, Iowa State University Ames, Iowa 50011-2064, U.S.A.

Bibliografia

• [1] L. Euler, Recherches sur une nouvelle espèce de carrés magiques, Mém. de la Societé de Vlissingue 9 (1779), pp.85 ff.
• [2] T. Evans, Homomorphisms of non-associative systems, J. London Math. Soc. 24 (1949), 254-260.
• [3] I.M. James, Quasigroups and topology, Math. Zeitschr. 84 (1964), 329-342.
• [4] H.O. Pflugfelder, Quasigroups and Loops: Introduction, Heldermann, Berlin, 1990.
• [5] A. Sade, Quasigroupes obéissant à certaines lois, Rev. Fac. Sci. Univ. Istanbul, Ser. A 22 (1957), 151-184.
• [6] J.D.H. Smith and A.B. Romanowska, Post-Modern Algebra, Wiley, New York, NY, 1999.
• [7] W. Taylor, Hyperidentities and hypervarieties. Aequationes Math. 23 (1981), 30-49.

Identyfikatory

DOI

10.7151/dmgaa.1116