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Apr
19
revised Writing equations without latex (for labelling, classification, structure analysis and rendering according to mathematical meaning)
edited tags
Apr
18
answered Finitely generated modules and submodules
Apr
15
revised Factorizing expressions
edited tags
Apr
14
comment Corollary to Maschke's Theorem.
@QiaochuYuan: That should be an answer.
Apr
14
comment Does this define a Ring?
For a non-trivial group it's never an integral domain. Consider the function that's just $1$ on all group elements and consider a function whose values when summed over the entire group yield zero.
Apr
13
comment Direct limit of quotient groups
Ah, right. Nevermind.
Apr
12
comment Direct limit of quotient groups
It looks like all the maps in your induced direct system are zero.
Apr
10
comment Find an automorphism
That doesn't respond to my comment.
Apr
10
comment Find an automorphism
Why does $\phi(a) = b$? You said $a = b^n$ and $\phi(a^j) = b^{jn}$. Plug in $j = 1$ and we get $\phi(a) = \phi(a^1) = b^{1n} = b^n = a$.
Apr
9
comment Find an automorphism
If $b^n = a$ then the map $\phi(a^j) = b^{jn}$ is the identity map and it doesn't map $a$ to $b$.
Apr
9
comment Find an automorphism
You need to explain what $a$, $b$, and $j$ are, otherwise that's just a random string of letters.
Apr
9
revised Help to understand and complete a proof of a theorem about nilpotent endomorphisms and Jordan-basis
deleted 2 characters in body
Apr
9
answered Find an automorphism
Apr
9
comment Direct limit sheaf.
You can't write them explicitly, they are given by sheafification of a map that's given by a universal property. You'll have to use universal properties to prove that the two compositions in your commutative diagram are identical.
Apr
9
answered $GL_3(\mathbb{F}_2)$ is simple
Apr
9
answered Direct limit sheaf.
Apr
8
comment Why are functors exact if they preserve all short exact sequences?
Modulo some size concerns which aren't relevant here, abelian categories are module categories so if you can prove the statement for module categories then you've proven it for abelian categories. See here or here.
Apr
8
comment Proof about the polynomial algebra(Friedberg, LA 4th edition
en.wikipedia.org/wiki/Summation
Apr
8
comment Proof about the polynomial algebra(Friedberg, LA 4th edition
Sorry, but if you don't have time to deal with summations then you don't have time to do this problem. Most people on this site are willing to help but are going to require that you put effort into this as well.