- Tytuł:
- Solution of Belousovs problem
- Autorzy:
-
Akivis, Maks
Goldberg, Vladislav - Powiązania:
- https://bibliotekanauki.pl/articles/728738.pdf
- Data publikacji:
- 2001
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
n-ary quasigroup
reducible
irreducible - Opis:
-
The authors prove that a local n-quasigroup defined by the equation
$x_{n+1} = F(x₁,...,xₙ) = (f₁(x₁) + ... + fₙ(xₙ))/(x₁ + ... + xₙ)$,
where $f_{i}(x_{i})$, i,j = 1,...,n, are arbitrary functions, is irreducible if and only if any two functions $f_{i}(x_{i})$ and $f_{j}(x_{j})$, i ≠ j, are not both linear homogeneous, or these functions are linear homogeneous but $f_{i}(x_{i})/x_{i} ≠ f_{j}(x_{j})/x_{j}$. This gives a solution of Belousov's problem to construct examples of irreducible n-quasigroups for any n ≥ 3. - Źródło:
-
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 1; 93-103
1509-9415 - Pojawia się w:
- Discussiones Mathematicae - General Algebra and Applications
- Dostawca treści:
- Biblioteka Nauki
Artykuł