Show that an element is irreducible but not prime.

139 Views Asked by At

Show that in the ring $\mathbb Q[x, y]/(x^3 -y^2)$ the element $x +(x^3 -y^2)$ is irreducible but not prime.

Not sure how to show this. I know that $(x^3 -y^2)$ is a prime ideal but I cannot continue. How should I proceed?