Question

Galois group of $x^4+x^3+1\in\mathbb Q[x]$

score 95 · Answer 1 · 2018-06-16 10:43:38

95

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Galois group of $x^4+x^3+1\in\mathbb Q[x]$

Published on 16 Jun 2018 - 10:43

score 243 · Answer 2 · 2026-03-24 22:01:50

243

Views

Is $\sqrt[3]5+\sqrt[3]7$ contained in a cyclotomic extension?

Published on 24 Mar 2026 - 22:01

score 494 · Answer 3 · 2018-06-16 11:32:54

494

Views

Galois Group of $x^6+3\in\mathbb F_7$

Published on 16 Jun 2018 - 11:32

score 196 · Answer 4 · 2026-03-25 11:13:43

196

Views

Finite field adjunction - isomorphism that maps from the field into a polynomial ring factored over an ideal

Published on 25 Mar 2026 - 11:13

score 282 · Answer 5 · 2018-06-17 02:06:57

282

Views

Fundamental Theorem of Galois Theory and correspondence between fields and subgroups.

Published on 17 Jun 2018 - 2:06

score 403 · Answer 6 · 2026-03-25 13:13:25

403

Views

Doubt in proof of Theorem 3.19 from Patrick Morandi's Field and Galois Theory

Published on 25 Mar 2026 - 13:13

score 363 · Answer 7 · 2018-06-17 21:27:00

363

Views

If $f(x) \in \mathbb{Q}[x]$ is a monic irreducible polynomial of degree $3$, then $f$ has no roots in $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$.

Published on 17 Jun 2018 - 21:27

score 150 · Answer 8 · 2018-06-17 21:49:55

150

Views

$|\mathbb{Q}(a):\mathbb{Q}|=n,|\mathbb{Q}(b):\mathbb{Q}| =m$ and $\gcd(m,n)=1 \implies|\mathbb{Q}(ab):\mathbb{Q}|=mn$

Published on 17 Jun 2018 - 21:49

score 230 · Answer 9 · 2018-06-19 11:06:26

230

Views

Galois extension with $X^4-2aX^2+b\in\mathbb Q[X]$

Published on 19 Jun 2018 - 11:06

score 35 · Answer 10 · 2018-06-19 14:33:10

35

Views

About the conjugates of an element

Published on 19 Jun 2018 - 14:33

score 269 · Answer 11 · 2018-06-20 01:45:21

269

Views

How to compute the degree of $\mathbb{Q}[\sqrt[3]{2}+\sqrt[5]{2}]$ over $\mathbb{Q}$?

Published on 20 Jun 2018 - 1:45

score 83 · Answer 12 · 2026-03-20 08:36:57

83

Views

Galois extension of exponent $mp^r$ in characteristic $p$

Published on 20 Mar 2026 - 8:36

score 161 · Answer 13 · 2026-03-24 23:46:32

161

Views

How to show that $\mathrm{Gal}(\Bbb Q(\xi_{p^n})/\Bbb Q(\xi_{p^m}))$ is cyclic?

Published on 24 Mar 2026 - 23:46

score 357 · Answer 14 · 2018-06-21 16:24:25

357

Views

How to show that $G=\mathrm{Gal}[\Bbb Q(\xi_{2^n})/\Bbb Q(\xi_{2^m})]$ cyclic?

Published on 21 Jun 2018 - 16:24

score 97 · Answer 15 · 2026-03-25 03:02:58

97

Views

Are there infinite extensions of $K$ inside $K^{ab}$ for $K$ local field?

Published on 25 Mar 2026 - 3:02

List Question

Galois group of $x^4+x^3+1\in\mathbb Q[x]$

Is $\sqrt[3]5+\sqrt[3]7$ contained in a cyclotomic extension?

Galois Group of $x^6+3\in\mathbb F_7$

Finite field adjunction - isomorphism that maps from the field into a polynomial ring factored over an ideal

Fundamental Theorem of Galois Theory and correspondence between fields and subgroups.

Doubt in proof of Theorem 3.19 from Patrick Morandi's Field and Galois Theory

If $f(x) \in \mathbb{Q}[x]$ is a monic irreducible polynomial of degree $3$, then $f$ has no roots in $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$.

$|\mathbb{Q}(a):\mathbb{Q}|=n,|\mathbb{Q}(b):\mathbb{Q}| =m$ and $\gcd(m,n)=1 \implies|\mathbb{Q}(ab):\mathbb{Q}|=mn$

Galois extension with $X^4-2aX^2+b\in\mathbb Q[X]$

About the conjugates of an element

How to compute the degree of $\mathbb{Q}[\sqrt[3]{2}+\sqrt[5]{2}]$ over $\mathbb{Q}$?

Galois extension of exponent $mp^r$ in characteristic $p$

How to show that $\mathrm{Gal}(\Bbb Q(\xi_{p^n})/\Bbb Q(\xi_{p^m}))$ is cyclic?

How to show that $G=\mathrm{Gal}[\Bbb Q(\xi_{2^n})/\Bbb Q(\xi_{2^m})]$ cyclic?

Are there infinite extensions of $K$ inside $K^{ab}$ for $K$ local field?

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