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- Title
Absorbent property, Krasner type lemmas and spectral norms for a class of valued fields.
- Authors
POPESCU, Sever Angel
- Abstract
Let (K,ҩ) be a perfect valued field of rank 1, let ҩ be an extension of the absolute (multiplicative) value ҩ to a fixed algebraic closure K and let ǁ.ǁ1193 be the corresponding spectral norm on K. Let (K,ǁ.ǁ1193) be a fixed completion of (K,ǁ.ǁ1193) In this paper we generalize a result of A. Ostrowski [8] relative to the absorbent property of a subfield, from the case of a complete non-Archimedian valued field of characteristic 0 to our ring (K,ǁ.ǁ1193) (see Theorem 1, Theorem 4). We also apply these results to discuss in a more general context the following conjecture due to A. Zaharescu (2009): 〈For any x,y ∊ Cp-the complex p-adic field, there exists t ∊ Qp-the p-adic number field, such that Qp(x,y) = Qp(x+ty), where L means the p-adic topological closure of a subfield L of Cp in Cp〉.
- Subjects
SPECTRAL theory; TOPOLOGY; P-adic fields; CLOSURE spaces; VALUED fields; GENERALIZATION
- Publication
Proceedings of the Japan Academy, Series A: Mathematical Sciences, 2013, Vol 89, Issue 10, p138
- ISSN
0386-2194
- Publication type
Article
- DOI
10.3792/pjaa.89.138