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Diskret bewertete perfekte Körper mit unvollkommenem Restklassenkörper. (German) Zbl 0016.05103
The paper begins with an exposition of the concepts of fields $$\mathbf K$$ with a discrete valuation, the valuation ring $$\mathbf I$$ of $$\mathbf K$$, the ideals $$(\pi^n)$$ of $$\mathbf I$$ where $$\pi$$ is a prime element of $$\mathbf I$$, and the residue-class field $$\mathbf F$$ of $$\mathbf K$$ modulo $$(\pi)$$. Let $$\mathbf F$$ be imperfect (unvollkommen) of characteristic $$p$$. Then $$\mathbf K$$ may have characteristic $$p$$ or zero. In the former case it is shown that $$\mathbf K$$ is the field of all power series with a finite number of negative exponents in an arbitrary prime $$\pi$$ over a subfield $$\mathbf T$$ equivalent to $$\mathbf F$$. In the latter case assume that $$\mathbf K$$ is complete (perfekt). Then there exists a complete unramified subfield of $$\mathbf K$$ with the same residue-class field as $$\mathbf K$$. But conversely to every imperfect field $$\mathbf F$$, there exists a complete unramified field of characteristic zero with $$\mathbf F$$ as residue-class field,

MSC:
 12J10 Valued fields
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