15/05/17 08:18:28.64 joHrS35r.net
>>431 つづき
ついでに (JS Milneは、例の人でしょうかね？ 余談だが、冒頭の番号体系がよくわからない・・)
URLﾘﾝｸ(mathoverflow.net)
What was Galois theory like before Emil Artin? edited May 31 '10
7
I read that the primitive element theorem for fields was fundamental in expositions of Galois theory before Emil Artin reformulated the subject.
What are the differences between pre and post-Artin Galois theory?
抜粋
9
Actually, it wasn't all that different, except that you first proved the primitive element theorem, and then proved things by choosing a primitive element.
Artin disliked having to make a choice, and his main contribution was show that you can do Galois theory without choosing a primitive element.
It's not obvious to me that this makes things easier or better. You can find the old approach in A.A. Albert's book on algebra. ? JS Milne May 31 '10 at 11:57
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Charles, the independence of multiplicative characters is usually credited to Dedekind. Galois theory is about separable extensions. ? JS Milne May 31 '10 at 13:11