I am studying algebraic geometry and I would like to know some technique to identify radical ideals. For instance, how do I know if the ideal $I=(x-4,y^2-x)$ is radical?
2026-04-25 19:55:31.1777146931
Technique to identify radical ideals
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Your ideal is $(x-4,y^2-4)=(x-4,(y-2)(y+2))$. It is contained in $(x-4,y-2)$ and $(x-4,y+2)$, both of which are prime — they are even maximal --- and equals their intersection. It follows that your ideal is radical.