Henselian valued fields with prescribed value group and residue field
نویسندگان
چکیده
منابع مشابه
On the Valued Function Fields with given Value Group and Residue Field or with given Residue Field and Genus
The valued function fields with given value group and residue field or with given genus and residue field are studied.
متن کاملUniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields
We give a de nition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp((t)), which works uniformly for all p and all nite eld extensions of these elds, and in many other Henselian valued elds as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modi cation of the language of Macintyre. Furthermore, we show the negative result th...
متن کاملRelative decidability and definability in henselian valued fields
Let (K, v) be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. The main step in obtaining this partition is an answer to the question, given a polynomial f(x) ∈ K[x], what is v(f(x))? Two applications are given: fir...
متن کاملAn Isomorphism Theorem for Henselian Algebraic Extensions of Valued Fields
In general, the value groups and the residue elds do not suuce to classify the algebraic henselian extensions of a valued eld K, up to isomorphism over K. We deene a stronger, yet natural structure which carries information about additive and multiplica-tive congruences in the valued eld, extending the information carried by value groups and residue elds. We discuss the cases where these \mixed...
متن کاملKummer subfields of tame division algebras over Henselian valued fields
By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [re...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0344234-2