The fundamental theorem on symmetric polynomials

Hamza E. S. Daoub

In this work we are going to extend the proof of Newton's theorem of symmetric polynomials, by considering any monomial order $>$ on polynomials in $n$ variables $x_{1},x_{2},\dots,x_{n}$ over a field $k$, where the original proof is based on the graded lexicographic order. We will introduce some basic definitions and propositions to support the extended proof.