What is the structure of $\mathbb{Z}[X,Y]/(X^2+Y^2-1)$ ? How can I prove that it is Noetherian Ring?
Edit: Here, $(X^2+Y^2-1)$ refers to ideal generated by the polynomial $p(X,Y)=X^2+Y^2-1$
2026-03-28 01:12:48.1774660368
How do I show that this quotient is a Noetherian Ring?
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There is surjection from $\Bbb Z[X,Y]$, which is Noetherian by Hilbert's basis theorem.