Polynomial Ideal

This is an Ideal formed from a set of Polynomials. They contain factorization and division algorithms.

• Division Algorithm for Polynomials
• Prime Factorization of Polynomials

Definition

A Ideal set $\mathbb{F}[x]$ of Polynomials with coefficients in $\mathbb{F}$ A polynomial $f\in \mathbb{F}[x]$ takes the form $f(x)=c_0+c_1{x}^1+\cdots +c_k{x}^k$

Theorems

• Alternative Characterization of Polynomial Ideal
• Polynomial Ideals are Subspaces