Geodesic
On linear representations of quasigroups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 113-118 
A. A. Gvaramia; B. I. Plotkin. On linear representations of quasigroups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 3, pp. 113-118. http://geodesic.mathdoc.fr/item/FPM_2009_15_3_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For homotopies of quasigroups, an analog of the fundamental theorem on homomorphisms does not hold in general. In this paper, we consider two approaches that allow one to obtain some analog of this theorem: the introduction of strict homotopies and the move from quasigroups to three-sorted quasigroups.

[1] Gvaramiya A. A., “Predstavleniya kvazigrupp i kvazigruppovye avtomaty”, Fundament. i prikl. mat., 3:3 (1997), 775–800 | MR | Zbl

[2] Plotkin B. I., Universalnaya algebra, algebraicheskaya logika i bazy dannykh, Nauka, M., 1991 | MR | Zbl

[3] Albert A. A., “Quasigroups. I”, Trans. Amer. Math. Soc., 54 (1943), 507–519 | DOI | MR | Zbl