[過去ﾛｸﾞ] ✧ ✦ ✧ 複素解析4 ✦ ✧ ✦ (1002ﾚｽ)

✧ ✦ ✧ 複素解析4 ✦ ✧ ✦ http://rio2016.5ch.net/test/read.cgi/math/1693984172/

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981: １３２人目の素数さん [sage] 2024/06/12(水) 06:33:21.36 ID:kQ+gVNo/ >>979 Let 𝐾 be a field and 𝑀 be an intermediate field between 𝐾 and 𝐾(𝑋) for some indeterminate X. Then there exists a rational function 𝑓(𝑋)∈𝐾(𝑋) such that 𝑀=𝐾(𝑓(𝑋)). In other words, every intermediate extension between 𝐾 and 𝐾(𝑋) is a simple extension. Proofs The proof of Lüroth's theorem can be derived easily from the theory of rational curves, using the geometric genus. This method is non-elementary, but several short proofs using only the basics of field theory have long been known, mainly using the concept of transcendence degree. Many of these simple proofs use Gauss's lemma on primitive polynomials as a main step. http://rio2016.5ch.net/test/read.cgi/math/1693984172/981

983: １３２人目の素数さん [sage] 2024/06/12(水) 08:27:55.68 ID:kQ+gVNo/ 柳老面 http://rio2016.5ch.net/test/read.cgi/math/1693984172/983

986: １３２人目の素数さん [sage] 2024/06/12(水) 18:26:38.75 ID:kQ+gVNo/ Rudinの本が有名なのは 最初に指数関数を用いたWeierstrassの 円周率の定義が書いてあるから http://rio2016.5ch.net/test/read.cgi/math/1693984172/986

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