Every Henselian field of residue characteristic 0 admits a truncation-closed embedding in a field of generalised power series (possibly, with a factor set). As corollaries we obtain the Ax–Kochen–Ershov theorem and an extension of Mourgues and Ressayre's theorem: every ordered field which is Henselian in its natural valuation has an integer part. We also give some results for the mixed and the finite characteristic cases.
Embedding Henselian fields into power series / Fornasiero, Antongiulio. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 304:(2006), pp. 112-156. [10.1016/j.jalgebra.2006.06.037]
Embedding Henselian fields into power series
Fornasiero, Antongiulio
2006
Abstract
Every Henselian field of residue characteristic 0 admits a truncation-closed embedding in a field of generalised power series (possibly, with a factor set). As corollaries we obtain the Ax–Kochen–Ershov theorem and an extension of Mourgues and Ressayre's theorem: every ordered field which is Henselian in its natural valuation has an integer part. We also give some results for the mixed and the finite characteristic cases.File in questo prodotto:
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