Question

Working on Galois Theory. Splitting field of f(x) = $x^2 + 11 \in Q[x]$

score 101 · Answer 1 · 2026-04-01 05:06:26

101

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Working on Galois Theory. Splitting field of f(x) = $x^2 + 11 \in Q[x]$

Published on 01 Apr 2026 - 5:06

score 148 · Answer 2 · 2019-04-23 09:56:16

148

Views

How to prove that $x\cdot y\neq 0$ when $x\neq 0$ and $y\neq0$ via field axioms?

Published on 23 Apr 2019 - 9:56

score 53 · Answer 3 · 2019-04-23 13:29:46

53

Views

Reducibility Unnecessary Hypothesis?

Published on 23 Apr 2019 - 13:29

score 101 · Answer 4 · 2019-04-24 14:55:09

101

Views

How to find the smallest degree polynomial from a family of polynomials?

Published on 24 Apr 2019 - 14:55

score 85 · Answer 5 · 2019-04-24 17:32:06

85

Views

How to remember n modulo m operations better?

Published on 24 Apr 2019 - 17:32

score 1k · Answer 6 · 2026-03-27 01:47:46

1k

Views

For any finite abelian group $G$, there is an integer $m$ with $G$ isomorphic to a subgroup of $U(\mathbb{Z}_{m})$.

Published on 27 Mar 2026 - 1:47

score 50 · Answer 7 · 2026-03-28 03:02:30

50

Views

If $[K:\Bbb{Q}]=2$ then $K=\Bbb{Q}(\sqrt{d})$.

Published on 28 Mar 2026 - 3:02

score 1.2k · Answer 8 · 2026-03-28 01:02:53

1.2k

Views

Proving that a field extension is Galois

Published on 28 Mar 2026 - 1:02

score 119 · Answer 9 · 2026-03-28 21:27:03

119

Views

$\mathbb{F}_p({\rm i}) = \mathbb{F}_{p^2}$ iff $p=3\mod 4$

Published on 28 Mar 2026 - 21:27

score 37 · Answer 10 · 2026-04-02 17:42:02

37

Views

Norm from $\overline{\Bbb Q}^* \to {\Bbb Q}*$

Published on 02 Apr 2026 - 17:42

score 148 · Answer 11 · 2026-04-01 06:30:49

148

Views

Infinitude of abelian extensions of $\mathbb{Q}$ with given Galois group $G$

Published on 01 Apr 2026 - 6:30

score 47 · Answer 12 · 2026-04-01 06:35:03

47

Views

Prove $\operatorname{Gal}(\mathbb{Q}(e^{\pi i/q}):\mathbb{Q}) \cong C_{q-1}$ for odd prime q.

Published on 01 Apr 2026 - 6:35

score 127 · Answer 13 · 2019-04-26 17:00:40

127

Views

Adjoining a transcendental element to an extension and a base field

Published on 26 Apr 2019 - 17:00

score 148 · Answer 14 · 2026-03-31 17:07:53

148

Views

Let $F = Z_5[x]/(x^3-x^2-1) = Z_5(u)$ where $u = [x]$ Give a basis for $F$ over $Z_5$

Published on 31 Mar 2026 - 17:07

score 258 · Answer 15 · 2019-04-26 18:37:18

258

Views

Let $\mathbb{R}^2$ be provided with component-wise multiplication $\cdot$ and component-wise addition $+$. Does $(\mathbb{R}^2,+,\cdot)$ form a field?

Published on 26 Apr 2019 - 18:37

List Question

Working on Galois Theory. Splitting field of f(x) = $x^2 + 11 \in Q[x]$

How to prove that $x\cdot y\neq 0$ when $x\neq 0$ and $y\neq0$ via field axioms?

Reducibility Unnecessary Hypothesis?

How to find the smallest degree polynomial from a family of polynomials?

How to remember n modulo m operations better?

For any finite abelian group $G$, there is an integer $m$ with $G$ isomorphic to a subgroup of $U(\mathbb{Z}_{m})$.

If $[K:\Bbb{Q}]=2$ then $K=\Bbb{Q}(\sqrt{d})$.

Proving that a field extension is Galois

$\mathbb{F}_p({\rm i}) = \mathbb{F}_{p^2}$ iff $p=3\mod 4$

Norm from $\overline{\Bbb Q}^* \to {\Bbb Q}*$

Infinitude of abelian extensions of $\mathbb{Q}$ with given Galois group $G$

Prove $\operatorname{Gal}(\mathbb{Q}(e^{\pi i/q}):\mathbb{Q}) \cong C_{q-1}$ for odd prime q.

Adjoining a transcendental element to an extension and a base field

Let $F = Z_5[x]/(x^3-x^2-1) = Z_5(u)$ where $u = [x]$ Give a basis for $F$ over $Z_5$

Let $\mathbb{R}^2$ be provided with component-wise multiplication $\cdot$ and component-wise addition $+$. Does $(\mathbb{R}^2,+,\cdot)$ form a field?

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