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The authors prove that a local n-quasigroup defined by the equation $x_{n+1}=F(x₁,...,xₙ)=(f₁\left(x₁\right)+...+fₙ\left(xₙ\right))/(x₁+...+xₙ)$, where $f_i\left(x_i\right)$, i,j = 1,...,n, are arbitrary functions, is irreducible if and only if any two functions $f_i\left(x_i\right)$ and $f_j\left(x_j\right)$, i ≠ j, are not both linear homogeneous, or these functions are linear homogeneous but $f_i\left(x_i\right)/x_i\ne f_j\left(x_j\right)/x_j$. This gives a solution of Belousov’s problem to construct examples of irreducible n-quasigroups for any n ≥ 3.

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.