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Diskriminanten und Picard-Invarianten freier quadratischer Erweiterungen

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Abstract

For commutative rings R, in which 2 is not a zero divisor, we give seven-term exact sequences, whose middle terms are the discriminant map or the Picard invariant of free quadratic extensions of R. As an application of our results we determine for all orders in quadratic number fields the group of free quadratic extensions and the group of quadratic extensions with normal basis.

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstr. 39, D - 8, München 2

    Rudolf Haggenmüller

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  1. Rudolf Haggenmüller
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Haggenmüller, R. Diskriminanten und Picard-Invarianten freier quadratischer Erweiterungen. Manuscripta Math 36, 83–103 (1981). https://doi.org/10.1007/BF01174814

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  • DOI: https://doi.org/10.1007/BF01174814

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