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I'm a student of mathematics in Germany.


Sep
30
awarded  Explainer
Sep
30
comment Free abelian groups in Algebraic Topolgogy
The free abelian group over a set $S$ is $\bigoplus_{S} ℤ$, sometimes written as $\bigoplus_{s ∈ S} ℤs$. It’s an abelian group in which $S$ is a $ℤ$-basis, that is you can uniquely write any element of the group as a linear combination of elements of $S$. Have you already had a look at what wiki has to say about this?
Sep
28
comment How to prove that every linear operator on a finite dimensional vector space is a sum of invertible linear operators
Nice. What happens if the base field is finite, though?
Sep
28
answered Cyclic space and commuting linear transforms
Sep
24
awarded  Autobiographer
Sep
23
accepted Example of a convex set whose closure is not convex?
Sep
23
asked Example of a convex set whose closure is not convex?
Sep
21
awarded  Yearling
Sep
20
comment How can I show that the tensor product of $\mathbb Z$ and $\mathbb R$ as $\mathbb Z$-modules is isomorphic to $\mathbb C$?
Uh, I was like “How can be ℂ, it’s ℝ!” – kind of a trick question, I guess.
Sep
7
comment Why is multiplication commutative - intuitive explanation
How about viewing the product $a·b$ as calculating the area of a rectangle with corresponding side lengths $a$ and $b$, and then viewing commutativity $a·b = b·a$ in that context as the fact that its area doesn’t change with a reflection of the rectangle?
Aug
30
comment Why $|G|$ even implies $|A(G)|$ also even?
@PtF Yeah, but that’d be a circular argument. It directly follows for any finite group $G$ that $A(G)$ has an even number of elements. The second statement is just a corollary and doesn’t have to be used (nor should it be) to again show that $|A(G)|$ is even.
Aug
25
comment How to proof homeomorphism between open ball and normic space
@MathewGeorge Both the function and its inverse are mentioned in the post – what do you mean?
Aug
22
comment Exercise on characterization of free abelian groups
@user113913 In that case you may also be interested in replacing the image-argument you have given to prove $f$ is epic by directly proving that both constructed arrows $f$, and the other $G → F$ are in fact inverse to each other. That would be bit more category-theoretic in flavour. (Your argument is of course perfectly fine, though.)
Aug
22
answered Exercise on characterization of free abelian groups
Aug
22
comment Exercise on characterization of free abelian groups
What is $ϕ$, though? Did you maybe mix up your names in the middle ant $ϕ$ is really $f$ and $f$ is really $h$?
Aug
13
revised How can I find $\mathbb Z_4$ as an extension of $\mathbb Z_2$ by $\mathbb Z_2$?
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Aug
13
revised How can I find $\mathbb Z_4$ as an extension of $\mathbb Z_2$ by $\mathbb Z_2$?
added 73 characters in body
Aug
13
revised How can I find $\mathbb Z_4$ as an extension of $\mathbb Z_2$ by $\mathbb Z_2$?
fixed definition of π
Aug
13
revised How can I find $\mathbb Z_4$ as an extension of $\mathbb Z_2$ by $\mathbb Z_2$?
added 382 characters in body
Aug
13
answered How can I find $\mathbb Z_4$ as an extension of $\mathbb Z_2$ by $\mathbb Z_2$?