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## On The Nilradical

Groups, Rings, Domains, Modules, etc, Galois theory
Tsakanikas Nickos
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### On The Nilradical

Let $\mathbb{K}$ be a field and let $A$ be a finitely generated $\mathbb{K}$-algebra. Show that the nilradical $\sqrt{0}$ of $A$ is the intersection of the maximal ideals of $A$ (which is the Jacobson radical $\mathfrak{R}(A)$ of $A$).