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Nov
7
comment An exercise related to Krull topology - showing that two bases define the same topology
@random123 - Could please you add some details ?
Nov
6
comment Subgroups of Index $2$ of $(\mathbb{Z}_{2})^{\aleph_{0}}$
@AsafKaragila - I mean the one group, up to isomorphism, of order $2$. I don't know about the dyadic integers (yet ?)
Nov
2
comment Checking irreducibility of a polynomial in $\mathbb{K}[x,y]$ and PAC fields
Thank you for posting an answer, I think there is a counter example for your claim: Take $K=\mathbb{R}$ and $\phi=-x^{2}$ which is separable as every irreducible factor is separable. $n=2$ and the $n$-th roots of unity are $\pm1\in\mathbb{R}$. $F(x,y)=y^{2}-\phi(x)=y^{2}+x^{2}=(y+ix)(y-ix)$ is a factorization over $\mathbb{C}$ so that $F(x,y)$ is not irreducible as claimed. Did I miss something ?
Nov
2
comment Proving that the maximal abelian extension contains all abelian extensions
I tried to correct my answer, I meant the product of the groups instead of the union. Does this seem ok ? I have sent an email for a further discussion, thanks!
Nov
1
comment Proving that the maximal abelian extension contains all abelian extensions
Thanks for posting an answer. I think I understand, but I'm not sure about all the details:Every algebraic extension is the composition of all the simple extensions generated by its elements, each of these extensions must be abelian since otherwise we can take two non commuting automorphisms of the Galois group of such simple extension and define then for the the above composition by fixing all other elements. This shows that each such simple extension is in the composition. Is that argument fine? I would also appreciate feedback about the first part of the exercise. Thanks again!
Oct
23
comment The cardinality of the union of two infinite sets of equal cardinality
You can't subtract infinite cardinals
Oct
6
comment Factorisation of polynomials without polynomial division
But why not use polynomial division?
Oct
4
comment Topology Book Recommendation
Yes, but the answers in that thread gave book names and explanations for their choices and I believe you have there the information you needed. Anyway, this is just my opinion
Oct
4
comment Topology Book Recommendation
Possible duplicate of Best book for topology?
Oct
1
comment If a subspace of $X^*$ is weak*-dense, does it separate points?
Do not "destroy" your own question.
Sep
24
comment Why consider neighbourhood containing an open set?
Are you asking about the source of the terminology or about proving that a neighbourhood of some point x is open ?
Sep
20
comment Doing extended synthetic division with more than 2 terms
google.co.il/…
Sep
20
comment Number of conjugates of an $m$-cycle $\sigma$ in $S_n$
But what is $m$ ?
Sep
4
comment A trick for calculating $n^6$ that I don't understand
And if anyone knows how to fix this spacing of the \mod..
Aug
30
comment Can 720! be written as the difference of two positive integer powers of 3?
Thanks for the explanation. This was a really nice solution!
Aug
30
comment Can 720! be written as the difference of two positive integer powers of 3?
Can you please explain the first congruence? I don't see where the $2^k$ came from
Aug
28
comment Is it possible to embed $\mathbb Z^n$ inside $ \mathbb Z^m$ as a $\mathbb Z$-module for $m < n$?
What exactly do you mean by linearly independent where we arn't talking about vector spaces ?
Aug
12
comment Mental Calculations
And given that the answer was probably an integer given the nature of the question, this really solved it the way I see it
Aug
10
comment Geometric or at least application view of a group with 3 elements?
How about rotation by 120 degrees?
Aug
7
comment $\sum_{n=1}^\infty a_n = \sum_{n=1}^\infty n a_n$ possible?
This assumes that the series is a positive series?