Uniformly defining $p$-henselian valuations

Autor:	Jahnke, Franziska, Koenigsmann, Jochen
Rok vydání:	2014
Předmět:	Mathematics - Logic Mathematics - Commutative Algebra Primary: 03C40 12E30. Secondary: 12L12 13J13 16W60
Druh dokumentu:	Working Paper
Popis:	Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable $p$-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical $p$-henselian valuation is uniformly 0-definable. We then apply this to show that there is a definable valuation inducing the ($t$-)henselian topology on any ($t$-)henselian field which is neither separably nor real closed. Comment: 13 pages, revised version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1407.8156 Zobrazit plný text záznamu View this record from Arxiv