Geodesic
Dickson's theorem for Bol loops
Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 297-301.

Voir la notice de l'article provenant de la source Math-Net.Ru

Dickson characterized groups in terms of one-sided invertibility. In this note, we give comparable characterizations for Bol and Moufang loops.
Keywords: left (right) Bol identity, left (right) quasigroup, loop, left (right) Moufang identity.
Mots-clés : quasigroup 
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Yuri Movsisyan. Dickson's theorem for Bol loops. Algebra and discrete mathematics, Tome 24 (2017) no. 2, pp. 297-301. http://geodesic.mathdoc.fr/item/ADM_2017_24_2_a8/

[1] V. D. Belousov, Foundations of The Theory of Quasigroups and Loops, Nauka, Moscow, 1967 (Russian) | MR

[2] G. Bol, “Gewebe und Gruppen”, Math. Ann., 114 (1937), 414–432 | DOI | MR

[3] L. E. Dickson, “Definitions of a group and a field by independent postulates”, Trans. Amer. Math. Soc., 6 (1905), 198–204 | DOI | MR | Zbl

[4] S. V. Matveev, “Distributive groupoids in knot theory”, Mat. Sb. (N.S.), 119:1 (1982), 78–88 | MR

[5] R. Moufang, “Zur struktur von Alternativkörpern”, Math. Ann., 10 (1935), 416–430 | DOI | MR

[6] Yu. M. Movsisyan, Introduction of The Theory of Algebras with Hyperidentities, Yerevan State University Press, Yerevan, 1986 (Russian) | MR

[7] Russian Math. Surveys, 53 (1998), 57–108 | DOI | DOI | MR | Zbl

[8] V. Pambuccian, “Euclidean geometry problems rephrased in terms of midpoints and point-reflections”, Elem. Math., 60 (2005), 19–24 | DOI | MR | Zbl

[9] H. O. Pflugfelder, Quasigroups and Loops, Introduction, Helderman Verlag, Berlin, 1990 | MR | Zbl

[10] J. H. Przytycki, “Knot and distributive homology: from arc colorings to Yang-Baxter homology”, New Ideas in Low Dimensional Topology, 2015, 413–488 | DOI | MR | Zbl

[11] Academic Press, New York, 1982 | MR | Zbl | Zbl

[12] L. A. Skornyakov, “Right alternative fields”, Izvestia Akad. Nauk SSSR, Ser. Mat., 15 (1951), 177–184 | MR | Zbl

[13] J. D. H. Smith, A. B. Romanowska, Post-Modern Algebra, Wiley, New York, 1999 | MR | Zbl