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Root continuity theorems in valued fields. (Russian, English) Zbl 1150.12003
Sib. Mat. Zh. 47, No. 6, 1258-1264 (2006); translation in Sib. Math. J. 47, No. 6, 1027-1033 (2006).
Summary: The literature on valued fields contains a series of theorems referred to as root continuity theorems. The goal of this article is to improve the constants $$\delta$$ for three available theorems formulated in the language of $$\varepsilon$$ and $$\delta$$. The proofs rest on the basic proposition of the author’s article [Izv. Math. 71, No. 6, 1079–1104 (2007; Zbl 1150.12001)].

##### MSC:
 12J10 Valued fields 12E05 Polynomials in general fields (irreducibility, etc.)
##### Keywords:
valued field; root continuity theorem
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