On Newton's identities in positive characteristic
arXiv:2305.19850 · doi:10.1016/j.jalgebra.2025.01.010
Abstract
Newton's identities provide a way to express elementary symmetric polynomials in terms of power polynomials over fields of characteristic zero. In this article, we study the failure of this relation in positive characteristic and what can be recovered. In particular, we show how one can write the elementary symmetric polynomials as rational functions in the power polynomials over any commutative unital ring.
arXiv commentFinal version, to appear in J. Alg