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I'm a student of mathematics in Germany.


Nov
16
revised is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
included note/warning
Nov
15
comment is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
@Lubin. Hm, why?
Nov
15
revised is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
added 26 characters in body
Nov
15
answered is $f(x)=x^4 +x^3 +x^2 +x +1$ irreducible in $R=(\mathbb Z/7\mathbb Z)[x]$?
Nov
15
comment Instructive sources for arguing without elements
@MartinBrandenburg You plan to write one? That’s great news! But how about graduate level books?
Nov
13
asked Instructive sources for arguing without elements
Nov
13
answered Show that there is an $R$-module homomorphism $\bar{h}$ such that $g \circ \bar{h} = h$.
Nov
13
comment Show that there is an $R$-module homomorphism $\bar{h}$ such that $g \circ \bar{h} = h$.
“We can let $A$ be the internal direct sum of the given submodules $P$ and $Q$” – Why? Why should $A = P \oplus Q$? I think $A$ is meant to be arbitrary.
Nov
11
answered Why is empty product defined to be $1$?
Nov
10
comment Is there any intuitive understanding of normal subgroup?
If you view subgroups of a group acting on some space as (possible) stabilizers, normal subgroups are those which stabilize not only points, but whole orbits. In that sense, they are global versions of subgroups.
Nov
9
comment Prove that a matrix and its inverse are over the same field
@user191052 Yes. This also generalizes to arbitrary rings.
Nov
9
answered Union of convex hulls
Nov
9
answered Prove that a matrix and its inverse are over the same field
Nov
8
comment Irrationality proof
Yes. If $\sqrt{7-\sqrt 2}$ was rational then so would be $\sqrt 2$, your proof is correct. (Only the square is $7 - \sqrt 2$.)
Nov
6
revised Is a set open in a product of spaces if all its segments are open in their factors?
added background
Nov
6
accepted Is a set open in a product of spaces if all its segments are open in their factors?
Nov
6
asked Is a set open in a product of spaces if all its segments are open in their factors?
Nov
3
comment Summation of the series$\sum_{n=1}^\infty\frac{1}{n^2+4}$
The summands don’t depend on any summation index so far, so the series will diverge. You should clarify. (Also, only use the dollars $ to encapsulate math.)
Nov
3
revised Summation of the series$\sum_{n=1}^\infty\frac{1}{n^2+4}$
deleted 7 characters in body; edited title
Oct
28
comment What is the space that we live in?
Very poetic title. I like that. As far as I know, there isn’t even consensus about its dimension.