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Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].

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a problem about field extension [closed]

Let K and L are fields,L is a sub field of K,and L is isomorphic to K,whether can we get K=L?If true,how to prove? Thanks. …
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a problem about field extension

If K and L are F-field extensions, K/F and L/F are both finite dimensional, and the isomorphism from K to L is an F-homomorphism, then the proof is easy, but the general case seems difficult.
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