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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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Existence of maximal totally ramified extensions of an arbitrary CDVF

The second sequence always split. This is proved in a paper by Kuhlmann, Pank, and Roquette, manuscripta mathematica 55 (1986), 39-77.
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