Necessary conditions of applicability of Gaussian elimination to systems of equations over quasigroups
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Sergey V. Polin
Abstract
Previously, in the process of investigating systems of equations over the given family đť”– of quasigroup operations, the author proved the following fact: applicability of Gaussian elimination to the systems considered requires that generalized distributivity and transitivity identities hold for the operations from đť”–. The present paper describes all sets of operations that satisfy these identities. The result obtained allows one to conclude that Gaussian elimination is applicable only if the system of equations is linear or may be reduced to a linear system.
Originally published in Diskretnaya Matematika (2018) 30, №1, 95–113 (in Russian).
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Articles in the same Issue
- Frontmatter
- Completeness criterion for the enumeration closure operator in three-valued logic
- Classification of distance-transitive orbital graphs of overgroups of the Jevons group
- Necessary conditions of applicability of Gaussian elimination to systems of equations over quasigroups
- The generalized complexity of linear Boolean functions
- On some implicitly precomplete classes of monotone functions in Pk
- Trees without twin-leaves with smallest number of maximal independent sets
- Limit theorems for some classes of power series type distributions
Articles in the same Issue
- Frontmatter
- Completeness criterion for the enumeration closure operator in three-valued logic
- Classification of distance-transitive orbital graphs of overgroups of the Jevons group
- Necessary conditions of applicability of Gaussian elimination to systems of equations over quasigroups
- The generalized complexity of linear Boolean functions
- On some implicitly precomplete classes of monotone functions in Pk
- Trees without twin-leaves with smallest number of maximal independent sets
- Limit theorems for some classes of power series type distributions
