# algebraic independence of elementary symmetric polynomials

###### Theorem.

Let $s_{1},s_{2},\dots,s_{n}$ be the elementary symmetric polynomials in $n$ variables $t_{1},t_{2},\dots,t_{n}$ over a commutative ring $R$. Then $s_{1},s_{2},\dots,s_{n}$ are algebraically independent elements of $R[t_{1},t_{2},\dots,t_{n}]$ over $R$.

Title algebraic independence of elementary symmetric polynomials AlgebraicIndependenceOfElementarySymmetricPolynomials 2013-03-22 14:49:11 2013-03-22 14:49:11 mclase (549) mclase (549) 5 mclase (549) Theorem msc 05E05