Jim
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 19h awarded Nice Answer Apr19 revised Writing equations without latex (for labelling, classification, structure analysis and rendering according to mathematical meaning) edited tags Apr18 answered Finitely generated modules and submodules Apr15 revised Factorizing expressions edited tags Apr14 comment Corollary to Maschke's Theorem. @QiaochuYuan: That should be an answer. Apr14 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. Apr13 comment Direct limit of quotient groups Ah, right. Nevermind. Apr12 comment Direct limit of quotient groups It looks like all the maps in your induced direct system are zero. Apr10 comment Find an automorphism That doesn't respond to my comment. Apr10 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 $\phi(a) = \phi(a^1) = b^{1n} = b^n = a$. Apr9 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 $b$. Apr9 comment Find an automorphism You need to explain what $a$, $b$, and $j$ are, otherwise that's just a random string of letters. Apr9 revised Help to understand and complete a proof of a theorem about nilpotent endomorphisms and Jordan-basis deleted 2 characters in body Apr9 answered Find an automorphism Apr9 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. Apr9 answered $GL_3(\mathbb{F}_2)$ is simple Apr9 answered Direct limit sheaf. Apr8 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. Apr8 comment Proof about the polynomial algebra(Friedberg, LA 4th edition en.wikipedia.org/wiki/Summation Apr8 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.