Finitely Generated Polynomial Ideal

Definition

Let $D=\{d_1,\dots ,d_n\}\subset \mathbb{F}[x]$ Then, the ideal generated by $D$ is the set $F[x]D=\{f\in F[x]|f=g_1{d}_1+\cdots +g_n{d}_n|g_i\in \mathbb{F}[x],\forall i\}$

If $D=\{0\}$, then $\mathbb{F}[x]D$ is the Trivial Ideal