Similar questions have come up on the last few past exam papers and I don't know how to solve it. Any help would be greatly appreciated..
Prove that the ideal of $\mathbb{Q}[X,Y]$ generated by $X^2(1+Y^3), Y^3(1-X^2), X^4$ and $ Y^6$ is a monomial ideal.
Hint. $(X^2(1+Y^3), Y^3(1-X^2), X^4, Y^6)=(X^2,Y^3)$.