Let $X, X_1, \dots, X_n$ be indetermiantes, $f \in \overline{K}[X_1, \dots, X_{n-2}, X]$ be an irreducible polynomial and $\mu \in \overline{K(X_{n-1},X_n)}$. Is it true that $f(X_1, \dots, X_{n-2}, \mu)$ is still irreducile over the field $\overline{K(X_{n-1},X_n)}$? I guess that this is true but I can't explain it rigorously. Can anybody help me?
2026-04-03 08:02:40.1775203360
Evaluating an irreducible polynomial in a trascendental element
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