What is $Spec R$ where $R$ is the integers modulo $6$? More generally, what are the techniques to find the spectrum of any commutative ring? (I would also be interested in the non-commutative case but this is secondary)
2026-04-01 16:42:44.1775061764
How do I find the spectrum of a ring?
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The (prime) ideals in a quotient such as $\mathbf Z/6\mathbf Z$ are in bijection with the (prime) ideals of $\mathbf Z$ that contain the ideal $6\mathbf Z $, i.e. with the prime divisors of $6$: $$\operatorname{Spec}R=\bigl\{2\mathbf Z/6\mathbf Z,3\mathbf Z/6\mathbf Z\}.$$