Geodesic
Families of quasigroup operations satisfying the generalized distributive law
Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 99-119
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The previous paper was concerned with systems of equations over a certain family $\mathcal S$ of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that the family $\mathcal S$ of quasigroups satisfy the generalized distributive law (GDL). In this paper we describe families $\mathcal S$ that satisfy GDL. The results are applied to construct classes of easily solvable systems of equations.
Keywords: systems of equations, Gaussian algorithm, quasigroups, generalized distributive law. 
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S. V. Polin. Families of quasigroup operations satisfying the generalized distributive law. Diskretnaya Matematika, Tome 30 (2018) no. 2, pp. 99-119. http://geodesic.mathdoc.fr/item/DM_2018_30_2_a7/

[1] Belousov V.D., Osnovy teorii kvazigrupp i lup, Nauka, Moskva, 1967 | MR

[2] Belousov V. D., “Systems of quasigroups with generalized identities”, Russian Math. Surveys, 20:1 (1965), 75–143 | DOI | MR | Zbl

[3] Glukhov M.M., “O metodakh postroeniya sistem ortogonalnykh kvazigrupp s ispolzovaniem grupp”, Matematicheskie voprosy kriptografii, 2:4 (2011), 5–24 | DOI

[4] Polin S.V., Elementarnye preobrazovaniya sistem uravnenii nad kvazigruppami i obobschennye tozhdestva., v pechati.

[5] Suprunenko D.A., Gruppy matrits, Nauka, Moskva, 1972 | MR

[6] Hosszú M., “Homogeneous groupoids”, Ann. Univ. Sci. Budapest. Eötvös // Sect. Math., 1960–1961, no. 3–4, 95–98 | MR