Elementary constructive theory of Henselian local rings
نویسندگان
چکیده
منابع مشابه
Elementary constructive theory of Henselian local rings
We give an elementary theory of Henselian local rings and construct the Henselization of a local ring. All our theorems have an algorithmic content.
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An introduction to the theme of local rings and Henselian local rings is given through numerous examples. We outline an elementary and effective construction of the Henselization of a local ring and an effective proof of about a classical result in Henselian local rings. This paper anounces a joint work of the three authors.
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This is a survey about the representation of positive semidefinite elements as sums of squares from a local viewpoint, in the sense of analytic geometry. Here, we present the most recent results in the more general frame of excellent henselian local rings with real closed residue field. 1
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We introduce an operational set theory in the style of [5] and [17]. The theory we develop here is a theory of constructive sets and operations. One motivation behind constructive operational set theory is to merge a constructive notion of set ([1], [2]) with some aspects which are typical of explicit mathematics [14]. In particular, one has non-extensional operations (or rules) alongside exten...
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We give model theoretic criteria for the existence of∃∀ and∀∃formulas in the ring language to define uniformly the valuation rings O of models (K,O) of an elementary theory Σ of henselian valued fields. As one of the applications we obtain the existence of an ∃∀-formula defining uniformly the valuation rings O of valued henselian fields (K,O) whose residue class field k is finite, pseudofinite,...
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ژورنال
عنوان ژورنال: Mathematical Logic Quarterly
سال: 2008
ISSN: 0942-5616
DOI: 10.1002/malq.200710057