If $F$ is an algebraic extension of a finite field $K$, then $F/K$ is separable. If we are able to show that $F/K$ is normal, then $F/K$ would be a Galois extension and hence splitting field of a polynomial over $K$, and therefore $F/K$ will be finite. But how to show $F/K$ is normal? Otherwise, if it is not so, give an example such that $K$ is a finite field and $F/K$ is algebraic but $[F:K]$ is infinite.
2026-02-23 01:07:05.1771808825
Every algebraic extension of a finite field is a finite extension. True or False?
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