I've read this proof:
Everything's clear except at the end where they said that if $\alpha$ is transcendental, then $I$ is the zero ideal.
How is that obvious?
2026-04-05 19:04:34.1775415874
Understanding proof with isomorphic field of fractions
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Recall that $\alpha$ is transcendental if there is no polynomial in $K[x]$ having $\alpha$ as a root. The kernel of $ev_\alpha$ by definition is then $\{0\}$ hence $I=(0)$.