Question

Isomorphic Galois groups imply isomorphic field extensions?

score 1.1k · Answer 1 · 2026-04-15 11:42:46

1.1k

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Isomorphic Galois groups imply isomorphic field extensions?

Published on 15 Apr 2026 - 11:42

score 1.2k · Answer 2 · 2026-04-13 21:46:36

1.2k

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Computing the degree of the splitting field of $x^3+18x+3$ over $\Bbb Q$

Published on 13 Apr 2026 - 21:46

score 51 · Answer 3 · 2016-05-02 15:28:43

51

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Find the minimum polynomial of $u$ over $Q$ where $u=\sqrt3-(1+(5/2)^{1/3})^{1/4}$

Published on 02 May 2016 - 15:28

score 82 · Answer 4 · 2026-04-16 20:44:02

82

Views

perfect squares in $\mathbb{Q}(\sqrt{2},\sqrt{91})$

Published on 16 Apr 2026 - 20:44

score 103 · Answer 5 · 2026-04-13 23:32:16

103

Views

Complex extension isomorphic to $\mathbb{R}$?

Published on 13 Apr 2026 - 23:32

score 141 · Answer 6 · 2026-04-13 07:56:40

141

Views

The fixed field of $A$ is equal to the fixed field of $\langle A\rangle$.

Published on 13 Apr 2026 - 7:56

score 1k · Answer 7 · 2026-04-11 13:07:20

1k

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When does a splitting field of a polynomial have the same degree as the polynomial?

Published on 11 Apr 2026 - 13:07

score 2.1k · Answer 8 · 2026-04-14 11:23:43

2.1k

Views

Why an absolutely irreducible representation is irreducible under all field extensions?

Published on 14 Apr 2026 - 11:23

score 44 · Answer 9 · 2026-04-16 01:58:43

44

Views

How to prove $t(x)-x\in F_{p}$ when $p(x) \in K$, $K$ a field whose characteristic is $p>0$

Published on 16 Apr 2026 - 1:58

score 500 · Answer 10 · 2026-04-17 05:13:53

500

Views

$\mathbb{R}[x]/\langle x^2+1\rangle$ and $\mathbb{R}[x]/\langle x^3 +x+1\rangle$ are isomorphic?

Published on 17 Apr 2026 - 5:13

score 2.1k · Answer 11 · 2026-04-15 03:34:22

2.1k

Views

Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.

Published on 15 Apr 2026 - 3:34

score 89 · Answer 12 · 2026-04-14 12:21:04

89

Views

Is this extension of the real numbers a field? It involves a unit of infinity.

Published on 14 Apr 2026 - 12:21

score 1.4k · Answer 13 · 2026-04-13 20:19:12

1.4k

Views

Fraleigh's proof of Kronecker's Theorem

Published on 13 Apr 2026 - 20:19

score 482 · Answer 14 · 2026-04-15 09:04:09

482

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What is the splitting field of $x^6+x^4-2x^2-2$ over $\mathbb{Q}$?

Published on 15 Apr 2026 - 9:04

score 80 · Answer 15 · 2026-04-14 04:02:37

80

Views

Is this a Galois extension?

Published on 14 Apr 2026 - 4:02

List Question

Isomorphic Galois groups imply isomorphic field extensions?

Computing the degree of the splitting field of $x^3+18x+3$ over $\Bbb Q$

Find the minimum polynomial of $u$ over $Q$ where $u=\sqrt3-(1+(5/2)^{1/3})^{1/4}$

perfect squares in $\mathbb{Q}(\sqrt{2},\sqrt{91})$

Complex extension isomorphic to $\mathbb{R}$?

The fixed field of $A$ is equal to the fixed field of $\langle A\rangle$.

When does a splitting field of a polynomial have the same degree as the polynomial?

Why an absolutely irreducible representation is irreducible under all field extensions?

How to prove $t(x)-x\in F_{p}$ when $p(x) \in K$, $K$ a field whose characteristic is $p>0$

$\mathbb{R}[x]/\langle x^2+1\rangle$ and $\mathbb{R}[x]/\langle x^3 +x+1\rangle$ are isomorphic?

Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.

Is this extension of the real numbers a field? It involves a unit of infinity.

Fraleigh's proof of Kronecker's Theorem

What is the splitting field of $x^6+x^4-2x^2-2$ over $\mathbb{Q}$?

Is this a Galois extension?

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