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Solution of Belousov's problem

Maks A. Akivis; Vladislav V. Goldberg — 2001

Discussiones Mathematicae - General Algebra and Applications

The authors prove that a local n-quasigroup defined by the equation $x_{n + 1} = F (x ₁, . . ., x ₙ) = (f ₁ (x ₁) + . . . + f ₙ (x ₙ)) / (x ₁ + . . . + x ₙ)$ , 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 $f_{i} (x_{i}) / x_{i} \neq f_{j} (x_{j}) / x_{j}$ . This gives a solution of Belousov’s problem to construct examples of irreducible n-quasigroups for any n ≥ 3.

О некоторых классах двойственно нормализованных поверхностей четырехмерного проективного пространства

Vladislav V. Goldberg; A. V. Čakmazjan — 1972

Commentationes Mathematicae Universitatis Carolinae

Algebraic aspects of web geometry

Maks A. Akivis; Vladislav V. Goldberg — 2000

Commentationes Mathematicae Universitatis Carolinae

Algebraic aspects of web geometry, namely its connections with the quasigroup and loop theory, the theory of local differential quasigroups and loops, and the theory of local algebras are discussed.

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Currently displaying 1 – 8 of 8

Solution of Belousov's problem

О некоторых классах двойственно нормализованных поверхностей четырехмерного проективного пространства

Algebraic aspects of web geometry

The Darboux mapping of canal hypersurfaces.

Contact co-isotropic CR submanifolds of a pseudo-Sasakian manifold.

Pseudo-Riemannian manifolds endowed with an almost para f-structure.

Pseudo-Sasakian manifolds endowed with a contact conformal connection.

Smooth lines on projective planes over two-dimensional algebras and submanifolds with degenerate Gauss maps.