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A twisted Laurent series ring that is a noncrossed product

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Abstract

The striking results on noncrossed products were their existence (Amitsur [1]) and the determination of ℚ(t) and ℚ((t)) as their smallest possible centres (Brussel [3]). This paper gives the first fully explicit noncrossed product example over ℚ((t)). As a consequence, the use of deep number theoretic theorems (local-global principles such as the Hasse norm theorem and density theorems) in order to prove existence is eliminated. Instead, the example can be verified by direct calculations. The noncrossed product proof is short and elementary.

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Authors and Affiliations

  1. Department of Mathematics, 0112, University of California at San Diego, 9500 Gilman Dr., 92093-0112, San Diego, CA, USA

    Timo Hanke

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  1. Timo Hanke
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Additional information

Supported in part by the DAAD (Kennziffer D/02/00701).

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Hanke, T. A twisted Laurent series ring that is a noncrossed product. Isr. J. Math. 150, 199–203 (2005). https://doi.org/10.1007/BF02762379

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  • DOI: https://doi.org/10.1007/BF02762379

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