Question

Let $~z=e^{\frac{2\pi i}{7}}~$ and $~\theta =z+z^2+z^4~$. Then...

score 580 · Answer 1 · 2026-03-26 17:53:50

580

Views

Let $~z=e^{\frac{2\pi i}{7}}~$ and $~\theta =z+z^2+z^4~$. Then...

Published on 26 Mar 2026 - 17:53

score 36 · Answer 2 · 2019-09-23 06:38:51

36

Views

$[E:F]$ and $[E':F']$ are coprime $\Longrightarrow [EE':F] = [E:F][E':F]$.

Published on 23 Sep 2019 - 6:38

score 82 · Answer 3 · 2026-03-28 06:10:20

82

Views

How to prove that prime $q \neq p$ isn't ramified in $\mathbb{Z}_p$-extension of $\mathbb{Q}$?

Published on 28 Mar 2026 - 6:10

score 136 · Answer 4 · 2026-03-26 03:11:20

136

Views

Finite dimensional splitting field is generated by finite number of polynomials

Published on 26 Mar 2026 - 3:11

score 67 · Answer 5 · 2019-09-26 21:15:05

67

Views

$α$ root of $f$, $β$ root of $g$. Show $f$ irred. in $\mathbb{Q}(β)$ iff $g$ irred. in $\mathbb{Q}(α)$

Published on 26 Sep 2019 - 21:15

score 34 · Answer 6 · 2019-09-27 14:30:18

34

Views

Proof about square roots of rational numbers being rational/irrational

Published on 27 Sep 2019 - 14:30

score 242 · Answer 7 · 2026-02-23 04:58:21

242

Views

Show that if $\beta \in E$ is algebraic over $F(\alpha)$, then there is a nonzero polynomial $f(x,y) \in F[x,y]$ such that $f(\alpha, \beta)=0$.

Published on 23 Feb 2026 - 4:58

score 590 · Answer 8 · 2026-03-25 22:22:54

590

Views

Tamely Ramified field extension of a Local Field

Published on 25 Mar 2026 - 22:22

score 536 · Answer 9 · 2026-03-25 04:58:45

536

Views

Minimal polynomial of root $\zeta_n$ over finite field $\mathbb{F}_p$

Published on 25 Mar 2026 - 4:58

score 323 · Answer 10 · 2014-03-11 18:08:25

323

Views

Does cyclic field imply Galois?

Published on 11 Mar 2014 - 18:08

score 1.7k · Answer 11 · 2014-03-12 12:52:53

1.7k

Views

Degree of extensions and their composite

Published on 12 Mar 2014 - 12:52

score 2.1k · Answer 12 · 2014-03-14 17:04:36

2.1k

Views

Prove subset of Field is a subfield

Published on 14 Mar 2014 - 17:04

score 151 · Answer 13 · 2014-03-14 23:45:33

151

Views

Characterizing $\operatorname{Gal}(\mathbb{Q}(\sqrt{p_1},\dots,\sqrt{p_n})/\mathbb{Q})$ for $p_i$ primes?

Published on 14 Mar 2014 - 23:45

score 286 · Answer 14 · 2026-03-27 15:07:28

286

Views

Why does irr(a,F(b)) divide irr(a,F)?

Published on 27 Mar 2026 - 15:07

score 998 · Answer 15 · 2014-03-19 20:34:03

998

Views

If $u,v \in K$ and $u+v$ is algebraic over $F$, is it true that $u$ is algebraic over $F(v)$?

Published on 19 Mar 2014 - 20:34

List Question

Let $~z=e^{\frac{2\pi i}{7}}~$ and $~\theta =z+z^2+z^4~$. Then...

$[E:F]$ and $[E':F']$ are coprime $\Longrightarrow [EE':F] = [E:F][E':F]$.

How to prove that prime $q \neq p$ isn't ramified in $\mathbb{Z}_p$-extension of $\mathbb{Q}$?

Finite dimensional splitting field is generated by finite number of polynomials

$α$ root of $f$, $β$ root of $g$. Show $f$ irred. in $\mathbb{Q}(β)$ iff $g$ irred. in $\mathbb{Q}(α)$

Proof about square roots of rational numbers being rational/irrational

Show that if $\beta \in E$ is algebraic over $F(\alpha)$, then there is a nonzero polynomial $f(x,y) \in F[x,y]$ such that $f(\alpha, \beta)=0$.

Tamely Ramified field extension of a Local Field

Minimal polynomial of root $\zeta_n$ over finite field $\mathbb{F}_p$

Does cyclic field imply Galois?

Degree of extensions and their composite

Prove subset of Field is a subfield

Characterizing $\operatorname{Gal}(\mathbb{Q}(\sqrt{p_1},\dots,\sqrt{p_n})/\mathbb{Q})$ for $p_i$ primes?

Why does irr(a,F(b)) divide irr(a,F)?

If $u,v \in K$ and $u+v$ is algebraic over $F$, is it true that $u$ is algebraic over $F(v)$?

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