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- W2060147189 abstract "In [R. Farré, A positivstellensatz for chain-closed fields R ( ( t ) ) and some related fields, Archiv der Mathematik 57 (1991), 446–455], R. Farré proved a positivstellensatz for real-series closed fields. Here we consider p -valued fields 〈 K , v p 〉 with a non-trivial valuation v which satisfies a compatibility condition between v p and v . We use this notion to establish the p -adic analogue of real-series closed fields; these fields are called henselian residually p - adically closed fields . First we solve a Hilbert’s Seventeenth problem for these fields and then we introduce the notions of residually p -adic ideal and residually p -adic radical of an ideal in the ring of polynomials in n indeterminates over a henselian residually p -adically closed field. Thanks to these two notions, we prove a Nullstellensatz theorem for this class of valued fields. We finish the paper with the study of the differential analogue of henselian residually p -adically closed fields. In particular, we give a solution to a Hilbert’s Seventeenth problem in this setting." @default.
- W2060147189 created "2016-06-24" @default.
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- W2060147189 date "2007-05-01" @default.
- W2060147189 modified "2023-09-29" @default.
- W2060147189 title "Henselian residually <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>p</mml:mi></mml:math>-adically closed fields" @default.
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- W2060147189 doi "https://doi.org/10.1016/j.jpaa.2006.06.015" @default.
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