Specific question: Let $F$ be a field and assume that $\mathbb{Q}$ is a proper subfield of $F$. Can $F$ be isomorphic to $\mathbb{Q}$?
Studying the foundaments of field theory I have to ask: Can a field be isomorphic to one of its proper subfields?
2026-03-28 08:28:15.1774686495
Fields and proper subfields.
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Yes, given any field $k$, $k(x)$ is isomorphic to $k(x^2)$.