نتایج جستجو برای: adic valuation
تعداد نتایج: 20930 فیلتر نتایج به سال:
in a commutative noetherian local complex normed algebra which is complete in its m-adic metric there are only finitely many closed prime ideals.
A well known theorem of Shuzo Izumi, strengthened by David Rees, asserts that all the divisorial valuations centered in an analytically irreducible local noetherian ring (R,m) are linearly comparable to each other. This is equivalent to saying that any divisorial valuation ν centered in R is linearly comparable to the m-adic order. In the present paper we generalize this theorem to the case of ...
We study the valuation at an irreducible polynomial v of the vadic power sum, for exponent k (or −k), of polynomials of a given degree d in Fq [t], as a sequence in d (or k). Understanding these sequences has immediate consequences, via standard Newton polygon calculations, for the zero distribution of corresponding v-adic Goss zeta functions. We concentrate on v of degree one and two and give ...
We prove that for p-optimal fields (a very large subclass of p-minimal fields containing all the known examples) a cell decomposition theorem follows from methods going back to Denef’s paper [Den84]. We derive from it the existence of definable Skolem functions and strong p-minimality, thus providing a new proof of the main result of [vdDHM99]. Then we turn to strongly p-optimal field satisfyin...
Generalizing and synthesizing earlier work on the model theory of valued difference fields and on the model theory of valued fields with analytic structure, we prove Ax-Kochen-Eršov style relative completeness and relative quantifier elimination theorems for a theory of valuation rings with analytic and difference structure. Specializing our results to the case of W [F p ], the ring of Witt vec...
1.1. The p-adic numbers. A rational number x ∈ Q× may be uniquely written as x = ab p n with a, b and n nonzero integers such that p ab. We define ordp(x) = n, |x|p = p−n, |0|p = 0. |·|p defines an absolute value on Q, satisfying the stronger ultrametric triangle equality |x+ y|p ≤ max(|x|p, |y|p). We define Qp to be the completion Q with respect to this metric and we use the same notation | · ...
The p-typical Witt vectors are a ubiquitous object in algebra and number theory. They arise as a functorial construction that takes perfect fields k of prime characteristic p > 0 to p-adically complete discrete valuation rings of characteristic 0 with residue field k and are universal in that sense. A. Dress and C. Siebeneicher generalized this construction by producing a functor WG attached to...
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