The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of algebraic relations found by the algorithm consists of polynomials having coefficients in the prime field F_p.

翻译：本文计算了有限域上初等对称多项式函数之间线性无关代数关系的数量。描述了一种能够找到所有这些关系的算法。证明了该算法所找到的代数关系理想的基由系数在素域F_p中的多项式组成。