Families of quasigroup operations satisfying the generalized distributive law
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Sergey V. Polin
Abstract
The previous paper was concerned with systems of equations over a certain family 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 𝓢 of quasigroups satisfy the generalized distributive law (GDL). In this paper we describe families 𝓢 that satisfy GDL. The results are applied to construct classes of easily solvable systems of equations.
Originally published in Diskretnaya Matematika (2019) 30, №2, 99–119 (in Russian).
References
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Articles in the same Issue
- Functional limit theorem for the local time of stopped random walk
- Investment Boolean problem with Savage risk criteria under uncertainty
- The complexity of checking the polynomial completeness of finite quasigroups
- Orthomorphisms of Abelian groups with minimum possible pairwise distances
- Families of quasigroup operations satisfying the generalized distributive law
- On weak positive predicates over a finite set
Articles in the same Issue
- Functional limit theorem for the local time of stopped random walk
- Investment Boolean problem with Savage risk criteria under uncertainty
- The complexity of checking the polynomial completeness of finite quasigroups
- Orthomorphisms of Abelian groups with minimum possible pairwise distances
- Families of quasigroup operations satisfying the generalized distributive law
- On weak positive predicates over a finite set
