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  • 0 posts edited
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  • 19 votes cast
Jun
27
comment The regular semisimple element in the algebraic group
If $K$ in the question is algebraically closed then any semisimple element $s$ can be diagonalized; it is regular if and only if all eigenvalues are distinct. This is equivalent, as Turgeon refers to Borel's book, to being outside the kernel of every root.
Jun
12
comment Need a hint to evaluate $\lim_{x \to 0} {\sin(x)+\sin(3x)+\sin(5x) \over \tan(2x)+\tan(4x)+\tan(6x)}$
The limit in your question can be evaluated by dividing the numerator and denominator by $x$ and then evaluating each separately.
Apr
10
accepted Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$?
Dec
23
awarded  Caucus
Oct
9
comment On Rieman integral
Taking square roots is a well-defined continuous (hence integrable) function.
Jun
6
revised A variation of Kuratowski closure-complement problem using dual cones
OP changed the question.
May
28
suggested rejected edit on A variation of Kuratowski closure-complement problem using dual cones
May
28
answered A variation of Kuratowski closure-complement problem using dual cones
Dec
23
awarded  Yearling
Feb
23
comment On the ring of integers of a compositum of number fields
Dear Bruno, can this solution be modified to find the ring of integers in case that none of $m$ and $n$ are 1 mod 4?
Feb
23
comment Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$?
Bruno, thanks; this seems a useful result to keep handy.
Feb
23
comment Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$?
Too bad if so.. :(
Feb
23
comment Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$?
Qiaochu, I have edited the question.
Feb
23
revised Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$?
added 4 characters in body
Feb
23
asked Computing the ring of integers of a number field $K/\mathbb{Q}$: Is $\mathcal{O}_K$ always equal to $\mathbb{Z}[\alpha]$ for some $\alpha$?
Aug
12
comment Find an ideal $I$ of $\mathbb{Z}[i]$ such that $\mathbb{Z}[i]/{I}$ is a field
What is R in the question?
Aug
12
answered Find an ideal $I$ of $\mathbb{Z}[i]$ such that $\mathbb{Z}[i]/{I}$ is a field
Jun
13
comment Let $X = \Bbb{R}$ with the discrete metric. Is $X$ connected?
@BrandonCarter There are stories of Emil Artin hurling a chalk or duster towards a student who'd ask ``What about the empty set?"
Jun
12
comment Is the sum and difference of two irrationals always irrational?
$\sqrt 2 - 1$ is irrational being the sum of a rational and an irrational.
Jun
12
comment Let $X = \Bbb{R}$ with the discrete metric. Is $X$ connected?
No discrete topology can ever be connected. You answer your own question. What do you mean by "formal way"?