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seen May 17 '13 at 19:44

I will usually wait a few days before accepting an answer.


Dec
7
awarded  Nice Question
May
20
awarded  Yearling
Mar
8
comment Curious about Hilbert-Zariski theorem involving homogeneous variety and set of zeroes.
@GeorgesElencwajg Would you be willing to include a citation for where this result appears in EGA?
Mar
7
accepted Deducing results in linear algebra from results in commutative algebra
Mar
7
comment Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
GitGud As written in your Edit1, you can only say that a sub-extension of degree 3 is isomorphic to $\mathbb{Q}(\sqrt[3]{2})$ if you already know that it's generated by a root of $X^3-2$, i.e. assuming what it is we were aiming to show.
Mar
7
accepted Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
Mar
4
comment Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
Anyway, the case of $[K:\mathbb{Q}]=3$ goes similarly; if $K$ contains a root of $X^3-2$ then we know what $K$ is, but if not then $[K(\sqrt[3]{3}):K]=3$, which is impossible.
Mar
4
comment Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
I don't quite see why your Edit is correct: is it really the case that every extension of degree $3$ is isomorphic to $\mathbb{Q}(\sqrt[3]{2})$? This can't be.
Mar
3
comment If $g$ is an element in an abelian group $G$ and $H\leqslant G$, must there exist an $n$ such that $g^n\in H$?
No. Consider $G = \mathbb{C}^\times$ and $H=\{1\}$. Consider any element $g\in \mathbb{C}$ such that $|g|=1$ but $g$ is not a root of unity. Note that such an element must exist for cardinal reasons.
Feb
21
comment American undergraduate applying overseas
You might be interested in this program as well as another option, or you could apply directly to any number of masters programs at various European universities. Usually a masters is required for PhD enrollment I think, but why not try asking people in the departments you're interested in working in to see what they recommend?
Feb
10
asked Determining subfields of $\mathbb{Q}(\zeta_3,\sqrt[3]{2})$ without Galois theory?
Dec
24
comment étale fundamental group as unification of galois theory and covering theory
@GeorgesElencwajg After a long enough time, none of us will be remembered. :)
Oct
4
awarded  Quorum
Jul
26
comment Irreducible Polynomials in Finite Fields
The situation is even slightly better; two finite fields of the same cardinal are in fact equal inside a fixed algebraic closure.
Jul
7
comment Graduate school self-doubt (currently an undergraduate)
You'll also be competing with applicants from outside the US, who usually have two additional years' worth of training (masters level). I would recommend also applying to masters programs outside of the US. Some of them even have funding for students, making the option much more realistic.
Jul
4
revised Deducing results in linear algebra from results in commutative algebra
Precised a bit the language of the question.
Jul
4
comment Deducing results in linear algebra from results in commutative algebra
@MartinBrandenburg Thanks for clarifying the question; it seems I had some trouble stating the question precisely. Maybe I should add it to the original post.
Jul
4
comment Deducing results in linear algebra from results in commutative algebra
Thanks for sharing these interesting and detailed pedagogical remarks.
Jul
4
comment Deducing results in linear algebra from results in commutative algebra
@rschwieb Note that the first example I give uses a result in module theory. E.g. "linear transformations correspond to matrices, because this is true for free modules" is a trivial deduction which isn't worth mentioning. I only meant to avoid getting responses like "but every $k$-vector space is a $k$-module, so everything comes from commutative algebra."
Jul
4
revised Deducing results in linear algebra from results in commutative algebra
Title was probably not so clear, fixed it