Mariano Suárez-Alvarez
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Aug
14
comment What, and how can, topological invariants can be computed from a space's algebra of functions?
Of course it is possible: the algebra determines the space $X$ completely (up to isomorphism in its category)—this is preciely what having an equivalence means— so anything you may want to know about $X$ can be seen in $A$ somehow.
Aug
14
comment Integral homology of real Grassmannian $G(2,4)$
Well, try to figure it out from the description of the cells. I'm pretty sure both of your sources describe the cells, not only their number!
Aug
14
comment Integral homology of real Grassmannian $G(2,4)$
The only way to do this is to describe explicitly the attaching maps. K owing the number of cells is not enough.
Aug
13
comment $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
If you replace in my example a field by $\mathbb Z$ exactly the sam conclusion holds. If you want $C$ to be non-finitely generated over $\mathbb Z$ just localize at any prime, for example.
Aug
13
comment $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
Why do you think I said that? I didn't: it is false, and my example, precisely, shows that it is false!
Aug
13
comment $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
Don't ask a new question: find a projective resolution!
Aug
13
comment $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
That dimensión is not infinite.
Aug
12
comment $n$th roots of entire functions
The $\sin$ function feels bad.
Aug
12
comment $n$th roots of entire functions
Why does the entire function have finitely mane zeroes?
Aug
12
comment Are vector bundles special cases of étale bundles?
Please add such clarifications to the body of the question.
Aug
12
comment Are vector bundles special cases of étale bundles?
What exactly do you mean by étale bundle?
Aug
12
answered Decide if a given set of monomials is a basis of a polynomial ring quotient
Aug
12
comment Galois group of a characteristic polynomial
Do you know what a splitting field is? The answer given by gap tells you the answer to your question!
Aug
11
comment $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
Matrix algebras are one of the simplest examples of separable algebras; that they are separable should be proven in pretty much every textbook on the subject! On the other hand, for B you can, for example, compute $Tor^{B\otimes_AB}(B,B)$ and see that it is nonzero in every degree: this implies at once that the projective dimension of B as a bimodule is infinite.
Aug
11
revised $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
added 87 characters in body
Aug
11
comment Isosceles triangle has the least perimeter among triangles on the same base with same area?
The question in the title is quite weird...
Aug
11
comment $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
If C/A is a separable field extension, then every subextension is also separable. This is because separability of field extensions can be checked element by element.
Aug
11
answered $A \subseteq B \subseteq C$ with $A \subseteq C$ separable and $pd_{B \otimes_A B}(B) = \infty$
Aug
11
comment Why there is no “Nobel Prize” in mathematics however it is one of the most important fields in sciences in the side of research?
You are every systematic about misspelling the guy's name!
Aug
10
comment Non-commutative Leibniz rule
@Benjamin, why don't you try proving it?!