Let $R=\mathbb{Z}[x,y]$ and $I=(y-x^2)R+(x-4)R$ is ideal $J$ prime ?
I tried to produce such $a,b$ that $ab \in J$ but $a,b \not\in J$ but can't find so far
2026-04-22 03:07:53.1776827273
Determine if an ideal is prime
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Hint: Consider the map $$\theta: R\to \mathbb Z\\x\mapsto 4\\y\mapsto 16$$
Can you show that it is a homomorphism? What is its kernel?