I have figured out that if $K/F$ be an algebraic extension , then does every F-homomorphism need not be an automorphism .
But I can't figure it out for in thee trasncendental case.
2026-04-02 12:27:05.1775132825
Let K/F be a transcendental extension , then does every F-homomorphism has to be an automorphism?
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Clearly $X \mapsto X^2$ is an $F$-algebra endomorpishm of $K=F(X)$ that is not an automorphism.