[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む25 [無断転載禁止]©2ch.net (716ﾚｽ)
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631(1): 現代数学の系譜11 ガロア理論を読む 2016/12/03(土)14:03 ID:6Rgz8i9T(25/41) AAS
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Finding a basis of an infinite-dimensional vector space? asked Nov 29 '11 at 16:30 InterestedGuest

2 Answers answered Jan 20 '12 at 19:25 Qiaochu Yuan

For many infinite-dimensional vector spaces of interest we don't care about describing a basis anyway; they often come with a topology and we can therefore get a lot out of studying dense subspaces, some of which, again, have easily describable bases.
In Hilbert spaces, for example, we care more about orthonormal bases (which are not Hamel bases in the infinite-dimensional case); these span dense subspaces in a particularly nice way.

4. answered Jan 20 '12 at 19:09 David Wheeler
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632: 現代数学の系譜11 ガロア理論を読む 2016/12/03(土)14:20 ID:6Rgz8i9T(26/41) AAS
>>631 ついで

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Ring of formal power series finitely generated as algebra? asked Jan 6 '13 at 13:44 user55354

I'm asked if the ring of formal power series is finitely generated as a K-algebra. Intuition says no, but I don't know where to start. Any hint or suggestion?

2 Answers

Let A be a non-trivial commutative ring. Then A[[x]] is not finitely generated as a A-algebra.
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