As the text states, it is true.
However, the map
$$\varphi:\mathbb Z \to \mathbb Z^2, n \mapsto (n, 0)$$
seems to be a counter example as $\varphi^{-1}(\mathbb Z\times\{0\})=\mathbb Z$.
2026-03-24 22:09:48.1774390188
Does a ring homomorphism necessarily induce a map of their spectrums?
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