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In particular, this applies to finite field extensions of K.

A field extension is a special case of ring extension.

A field extension generated by the complete factorisation of a polynomial.

The number of algebraically independent transcendental elements in a field extension.

But this is a cyclic field extension, and so must contain a primitive root of unity.

Also in this case, twisted curves are isomorphic over the field extension given by the twist degree.

Alternatively, constructing such field extensions can also be done, if a bigger container is already given.

One can then view morphisms in Field as field extensions.

Minimal polynomials are useful for constructing and analyzing field extensions.

Given a field extension, one can "extend scalars" on associated algebraic objects.