Easy# Sets that are Ideals in Rings of Polynomials

ABSALG-LAKYQO

Recall that an ideal ${\mathcal I}$ in a *commutative* ring $R$ is a subring of $R$ such that for all $r \in R$ and all $\iota \in{\mathcal I}$, we have $r\iota\in{\mathcal I}$.

Let $k$ be a field and $R=k[x,y,z]$ be the ring of polynomials in $3$ variables with coefficients in $k$.

Let $k^3$ be the set of ordered triples $(a,b,c)$ with $a,b,c\in k$.

Which of the following subsets of $R$ forms an ideal in $R$?

Select **ALL** that apply.