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. 
@article{DM_2018_30_2_a7,
     author = {S. V. Polin},
     title = {Families of quasigroup operations satisfying the generalized distributive law},
     journal = {Diskretnaya Matematika},
     pages = {99--119},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2018_30_2_a7/}
}
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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/