http://swrc.ontoware.org/ontology#UnrefereedArticle
Note on Relatively Complete Fields
en
Inaba, Eizi
A real-valued function V(a) of a field k is a non-archimedean valuation V of k, if the relations V(ab)=V(a)+V(b) and V(a+b)≧Min {V(a), V(b)} hold, where we put V(0)=∞. The set of all elements a with V(a)≧0 is the valution ring R in k. All elements a with V(a)>0 form a prime ideal P in R. A polynomial f(x) with coefficients from R is called primitive, if among these coefficients there exists at least one unit. By Ostrowski the field k is termed relatively complete with respect to V, if Hensel's lemma holds for every primitive polynomial. The present note aims to reveal some characteristic properties of this field.
お茶の水女子大學自然科學報告
3
5-9
1952-07
00298190
AN00033958
application/pdf
400
お茶の水女子大学
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