Apparently any finite extension of a field with characteristic 0 is of the form $F(a)$ for some algebraic $a$. But wouldn't this mean that any two zeros of a polynomial (e. g. over $\mathbb{Q}$) would be linearly dependent (since the splitting field is a finite extension)?
2026-03-26 01:26:59.1774488419
Question about finite extensions and splitting fields
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