We have 2n\plus{}1 elements in the commutative ring R: α,α1,...,αn,ϱ1,...,ϱn. Let us define the elements \sigma_k\equal{}k\alpha \plus{} \sum_{i\equal{}1}^n \alpha_i\varrho_i^k . Prove that the ideal (σ0,σ1,...,σk,...) can be finitely generated.
L. Redei superior algebrasuperior algebra unsolved