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Abelsche Galoiserweiterungen von R[X]

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Abstract

Our main result states that for a commutative ring R and a finite abelian group G the following conditions are equivalent: (a) Gal(R,G)=Gal (R[X],G), i.e. every commutative Galois extension of R[X]with Galois group G is extended from R. (b) The order of G is a non-zero-divisor in R/Nil(R). The proof uses lifting properties of Galois extensions over Hensel pairs and a “Milnor-type” patching theorem.

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstraße 39, D-8000, München 2

    Cornelius Greither & Rudolf Haggenmüller

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  1. Cornelius Greither
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  2. Rudolf Haggenmüller
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Greither, C., Haggenmüller, R. Abelsche Galoiserweiterungen von R[X]. Manuscripta Math 38, 239–256 (1982). https://doi.org/10.1007/BF01168593

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  • DOI: https://doi.org/10.1007/BF01168593

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