[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む78 (1002ﾚｽ)
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266(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/10/27(日)12:32 ID:EUeYkluT(6/14) AAS
つづき

分岐（Ramification）の話
外部ﾘﾝｸ:en.wikipedia.org
Algebraic number field
(抜粋)
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q.

The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
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268: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/10/27(日)12:34 ID:EUeYkluT(8/14) AAS
>>266

つづき

An example
The following example illustrates the notions introduced above. In order to compute the ramification index of Q(x), where

f(x) = x^3 - x - 1 = 0,
at 23, it suffices to consider the field extension Q23(x) / Q23. Up to 529 = 232 (i.e., modulo 529) f can be factored as

f(x) = (x + 181)(x^2 - 181x - 38) = gh.
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