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non-abelian group of order 9
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6 votes
3 answers
208 views

Degree of extension $\Bbb Q(\sqrt[4]{5},\sqrt[6]{7})$.

6 votes
1 answer
252 views

Find an example of degree-100 extension of $\Bbb Q(\zeta_5)$ and $\Bbb Q(\sqrt[3]{2})$.

5 votes
2 answers
626 views

Understanding the graphic proof of homotopy

5 votes
1 answer
1k views

Understanding th proof of Hatcher 1.2.11

5 votes
1 answer
306 views

Prove that an open subfunctor of a scheme is itself a scheme

3 votes
1 answer
196 views

Prove that $\Bbb C[x,y]/\langle xy-1\rangle]\cong\Bbb C[s,t]/\langle s^2+t^2-1\rangle$

3 votes
0 answers
259 views

If $E/F$ is a Galois extension with abelian Galois group, then $E$ is a tower of quadratic extension iff $[E:F]$ is a power of $2$

3 votes
1 answer
436 views

Find the minimal polynomial of $\zeta_9+\zeta^{-1}_9$ over $\Bbb Q$

3 votes
4 answers
1k views

Prove that $x^4-2x^2-11$ is irreducible over $\Bbb Q$

2 votes
2 answers
136 views

How to formally prove that the degree of $\Bbb Q(\sqrt[5]{6},\sqrt[3]{7})$ is $15$?

2 votes
1 answer
103 views

(Proof Explanation) $\Bbb Q(\sqrt d)$ is never isomorphic to $\Bbb Q(\sqrt {d'})$ as fields

2 votes
1 answer
147 views

How can I see $\Phi_{p^r}(x)=(x^{p^{r-1}})^{p-1}+(x^{p^{r-1}})^{p-2}+\cdots+(x^{p^{r-1}})+1$ and is irreducible?

2 votes
1 answer
271 views

Necessary and sufficient conditions on m and n for $\Bbb F_{p^n}$ to have a subfield isomorphic with $F_{p^m}$. [duplicate]

2 votes
1 answer
2k views

Local degree of induced map $\hat{f}$ on Riemann surface for a polynomial $f$

2 votes
1 answer
394 views

Compute Tensor product $\Bbb Z[x]/\langle x^2\rangle \otimes \Bbb Z[y]/\langle y^2\rangle$

2 votes
3 answers
106 views

Show that $\sqrt[4]{28} + i\sqrt[4]{28} \;=\; 2\sqrt[4]{-7}$

2 votes
2 answers
406 views

Very detailed book for topological K-theory

2 votes
1 answer
57 views

Prove that $\Bbb Q[x]/\langle x^2+(x^3-1)^2-4\rangle$ is reduced

1 vote
1 answer
629 views

Prove $x^n-a$ is irreducible over $\Bbb Q(\zeta_n)$

1 vote
1 answer
437 views

How many elements are there in $\Bbb P_\Bbb Z^n(C)$ for $C=\Bbb Z/m\Bbb Z$($m\ge 1$)?

1 vote
0 answers
31 views

There is a ring homomorphism of F into E when$|E|$ is not a power of $|F|$

1 vote
2 answers
91 views

Can $\sqrt{3}$ be written as a polynomial expression in $\sqrt[3]{3}$ and $\zeta_3$

1 vote
2 answers
50 views

Why there may not be a $n$-th primitive root in splitting fields of $x^n-1$ of positive characteristic?

1 vote
1 answer
44 views

Questions about proving $E^H /F$ is a normal extension $\Leftrightarrow$ $H\lhd Gal(E/F)$

1 vote
1 answer
139 views

Prove that if $\alpha+\beta=\beta$, then $\alpha\le \beta$ [closed]

1 vote
1 answer
52 views

Proof verification: For any ordinals $\gamma,\beta$, $\gamma\le \gamma+\beta$.

1 vote
1 answer
460 views

Difference between "algebraically closed field" and the "relatively algebraically closed field"?

0 votes
3 answers
76 views

Prove that the function $f:\Bbb N \rightarrow \Bbb N,$ defined by $f(n)=6\lceil \frac{n}{3} \rceil -n-2$ is surjective.

0 votes
0 answers
66 views

Which of the following is a degree-100 extension of $\Bbb Q(i)$?

0 votes
2 answers
81 views

Can we prove that if the sequence is not bounded, then for any $n\in \Bbb N $ we have $|x_n|\ge n$