Polynomial rings of two variables

Question

Prove that $(x,y)$ is not a principal ideal in $\mathbb{Q}[x,y]$.

Here what is the definition of $(x,y)$? I don't know how to start the solution since I don't know the meaning of $(x,y)$.

Answer 1

It is the ideal generated by $\{x,y\}$. Explicitly, $(x,y)$ consists of those polynomials whose constant term is zero.

Hint for the exercise: If $(x,y)=(g)$, then show that $g$ is a gcd of $x$ and $y$. But $x$ and $y$ are coprime.