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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].

31 votes
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Is every field the field of fractions of an integral domain?

But no algebraic extension of $\mathbb F_p$ is, since its only subrings are fields. …
Robin Chapman's user avatar
10 votes

Fields with trivial automorphism group

Indeed this is the case for all number fields (finite extensions of $\mathbb{Q}$). …
Robin Chapman's user avatar
20 votes
Accepted

Is completeness of a field an algebraic property?

This is not complete under the $p$-adic metric, but it is isomorphic as a field to the complex numbers $\mathbb{C}$ which is complete under the standard metric (as both fields are algebraically closed …
Robin Chapman's user avatar