MODNET
Research Training Network in Model Theory
 Publications > Preprint server > Preprint Number 615 Preprint Number 615 615. Krzysztof Krupinski Superrosy fields and valuations E-mail: (email address protected by JavaScript. Please enable JavaScript to contact) Submission date: 15 August 2013. Abstract: We prove that every non-trivial valuation on an infinite superrosy field of positive characteristic has divisible value group and algebraically closed residue field. In fact, we prove the following more general result. Let K be a field such that for every finite extension L of K and for every natural number n>0 the index [L^*:(L^*)^n] is finite and, if char(K)=p>0 and f: L \to L is given by f(x)=x^p-x, the index [L^+:f[L]] is also finite. Then either there is a non-trivial definable valuation on K, or every non-trivial valuation on K has divisible value group and, if char(K)>0, it has algebraically closed residue field. In the zero characteristic case, we get some partial results of this kind. We also notice that minimal fields have the property that every non-trivial valuation has divisible value group and algebraically closed residue field. Mathematics Subject Classification: 03C60, 12J10 Keywords and phrases: Full text arXiv 1308.3394: pdf, ps.

 Last updated: August 28 2013 12:15 Please send your corrections to: The e-mail address is protected, enable Javascript to see it