現代数学の系譜11 ガロア理論を読む8at MATH
現代数学の系譜11 ガロア理論を読む8 - 暇つぶし2ch16:現代数学の系譜11 ガロア理論を読む
13/03/31 21:06:53.93
>>12
「ヘンゼルの補題」は、英語版の方がはるかに分かりやすいね
というか、内容が相当違う。英語版を読むべき

URLリンク(en.wikipedia.org)
In mathematics, Hensel's lemma, also known as Hensel's lifting lemma, named after Kurt Hensel, is a result in modular arithmetic,
stating that if a polynomial equation has a simple root modulo a prime number p,
then this root corresponds to a unique root of the same equation modulo any higher power of p, which can be found by iteratively "lifting" the solution modulo successive powers of p.
More generally it is used as a generic name for analogues for complete commutative rings (including p-adic fields in particular) of the Newton method for solving equations.
Since p-adic analysis is in some ways simpler than real analysis, there are relatively neat criteria guaranteeing a root of a polynomial.


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