Mariano Suárez-Alvarez
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4h
comment Solvable equivalent to nilpotency of first derived Lie algebra?
Indeed. Lie's theorem gives you a flag of ideals in the adjoint rep which the rep preserves, and elements in the derived subalgebra push things one level deeper.
4h
comment Solvable equivalent to nilpotency of first derived Lie algebra?
As for a reference, this should be in any sensible textbook!
9h
comment Existence of a non-abelian group of order $p^n$.
If you construct a nonabelian group of order p^3, the you can just do a direct product with a cyclic group of order $p^{n-3}$.
1d
comment Morita equivalence and right and left ideals of a Ring
I still don't understand. In fact, the explanation in your comment is less comprehensible to me that the original question. I don't know what you mean by Morita equivalence applying «to that case».
1d
comment Morita equivalence and right and left ideals of a Ring
«you conclude that right ideals of $M_n(R)$ are the same thing as submodules of $R^n$ as a right $R$-module» I don t understand this. "The same thing" means something unorthodox here :-)
1d
comment Morita equivalence and right and left ideals of a Ring
I do not understand what you are asking: what do you mean by «Morita theory applies to subrings»?
1d
comment Does naturality for characteristic classes imply the classifying space is universal for them?
Restricting along $G^\delta\to G$ which, which is a map of topological groups, you get a morphism in cohomology going the other way $H^*(G)\to H^*(G^\delta)$. Anything natural would have to be the composition of this with a map $H^*(\mathfrak g)\to H^*(G)$, and in good cases these two are isomorphic.
May
27
comment $S^2$ with countably many points removed is path-connected
You can do the general case with lines too.
May
26
comment Exercise about an algebraic surface
Is the intersection of four smooth quadrics in $P^6$ automatically smooth?
May
24
comment Find an arbitrary power of a lower triangular matrix of size $3\times 3$
This is a trivial matter using induction, really. I doubt there is any gain going in any other route...
May
24
comment Why should statistics be considered mathematics?
What does «being together» even mean?
May
23
answered Is parallel transport injective?
May
23
comment In (relatively) simple words: What is an inverse limit?
@AsafKaragila the claim that diagrams never help is uncharacteristically absurd coming from you...
May
22
comment simplicial homology definition
'\mathring\Delta' gives $\mathring\Delta$
May
22
comment Equivalence between category of $R$-modules and $S$-modules
@MartinBrandenburg, of course it is wrong. There do exist isomorphisms. Can you give an example relevant to this question?
May
22
comment If $M\bigoplus N $ submodule $A\bigoplus B$ does it imply either $M$ submodule $A$ or $M$ submodule $ B$
If it seems «very obvious» you should declare example hunting season started, for your intuition needs series adjusting!
May
22
answered Equivalence between category of $R$-modules and $S$-modules
May
22
comment Equivalence between category of $R$-modules and $S$-modules
One would usually only consider equivalences, as isomorphisms of categories are mostly nonexistent in nature — and then the rings need not be isomorphic; the keyword for this is «Morita equivalence».
May
22
comment What are Products and Quotients of vector space used for?
"Done Right" does not include giving a motivation!?
May
21
comment When does covering preserve rational cohomology?
Having tangent bundle with zero Pontriagin classes, for example, is a property of smooth manifolds which is a topological condition, and that is a significant theorem — and its significance, of course, is, precisely that there is a non-trivial content in claiming that a condition on the tangent bundle is topological.