Families of quasigroup operations satisfying the generalized distributive law

S. V. Polin

Academy of Cryptography of Russian Federation

Abstract: 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.

UDC: 519.548.74

Received: 01.11.2017
Revised: 28.04.2018

DOI: 10.4213/dm1519

 English version: Discrete Mathematics and Applications, 2020, 30:3, 187–202

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