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.
متن کاملHenselian Local Rings: Around a Work in Progress
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.
متن کاملSums of squares in excellent henselian local rings
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
متن کاملDefinable Henselian Valuation Rings
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,...
متن کاملExistential ∅-Definability of Henselian Valuation Rings
In [1], Anscombe and Koenigsmann give an existential ∅-definition of the ring of formal power series F [[t]] in its quotient field in the case where F is finite. We extend their method in several directions to give general definability results for henselian valued fields with finite or pseudo-algebraically closed residue fields. §
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ژورنال
عنوان ژورنال: Collectanea Mathematica
سال: 2016
ISSN: 0010-0757,2038-4815
DOI: 10.1007/s13348-016-0184-0