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seen Jan 19 at 15:42

Oct
5
awarded  Notable Question
Oct
3
comment example of use of (co)homology
Thanks! The book briefly mentions that cohomology relates universal covering and fundamental group, but don't mention examples such you told me.
Oct
3
comment example of use of (co)homology
The book is Japanese one, I think it's not famous. Yes, I learned the fundamental group.
Oct
3
asked example of use of (co)homology
Sep
24
awarded  Autobiographer
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awarded  Curious
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26
awarded  Critic
May
17
revised simple modules over non commutative polynomial rings
added 2 characters in body
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17
asked simple modules over non commutative polynomial rings
Feb
28
awarded  Popular Question
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15
awarded  Yearling
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6
comment Are two different prime ideals relatively prime?
I got it, thanks!
Dec
5
comment Are two different prime ideals relatively prime?
oh..., I forgot that $(0)$ is prime. Thanks!
Dec
5
asked Are two different prime ideals relatively prime?
Nov
3
awarded  Tumbleweed
Oct
27
asked Does a rectangle exists on any closed curve?
Sep
26
comment a base for a Galois group
Let $(G_{i})_{i\in I}$ be a projective system in which the $G_{i}$ are finite groups and endowed with the discrete topology. Every subsets of $G_{i}$ are open. The topology of $\prod G_{i}$ is defined as the product topology. The open sets of this set looks like $\prod S_{i}$, $S_{i}=G_{i}$ without finitely many $i\in I$. The topology on $\varprojlim G_{i}$ is the induced topology. This group is closed in $\prod G_{i}$.
Sep
25
comment a base for a Galois group
I forgot to insert "open subset". I understand the topology as the following. Gal$(L/K)\cong \varprojlim_{E\in I}$Gal$(E/K)$ as groups. The right side is considered as a profinite group and this defines the topology of the left side.
Sep
25
comment a base for a Galois group
Let $U\subset G$ and $x\in U$. I want to find $\sigma$ and $F$ such that $x\in U_{\sigma, F}\subset U$ but I can't do this. Denote by $I$ the set of subfields $E$ of $L$ which $E$ is a finite Galois extension of K. Since $U$ is open, there exists a finite subset $I'$ of $I$ and $U=\prod_{E} U_{E}$, if $E\in I-I',U_{E}=Gal(E/K)$, if $E\in I'$, $U_{E}\subset Gal (E/K)$. I expect that $F$ is determined by $\{U_{E}\}_{E\in I'}$ but I don't come up with the way to find $F$.
Sep
25
comment a base for a Galois group
I can't prove this and I have little intuition that $U_{\sigma, F}$ form a base for the open sets of $G$.