Is there an example of a field $K$ of characteristic 0 that has two commuting automorphisms f and g that cannot be extended to some automorphisms $\tilde{f}$ and $\tilde{g}$ on the algebraic closure $\bar{K}$ so that $\tilde{f}$ and $\tilde{g}$ would still commute?
2026-03-26 22:31:25.1774564285
Example of commuting field automorphisms that don't extend to algebraic closure?
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