Question

Factorization on an arbitrary field

score 36 · Answer 1 · 2026-03-25 09:33:39

36

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Factorization on an arbitrary field

Published on 25 Mar 2026 - 9:33

score 161 · Answer 2 · 2026-03-25 12:23:59

161

Views

Proof that $[\overline{\mathbb Q}:\mathbb R\cap\overline{\mathbb Q}]=2$

Published on 25 Mar 2026 - 12:23

score 11.2k · Answer 3 · 2026-03-25 06:03:29

11.2k

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prove that if $a=b$ then $a+c=b+c$ where $a,b,c\in \mathbb R$

Published on 25 Mar 2026 - 6:03

score 287 · Answer 4 · 2026-03-25 23:52:25

287

Views

$\zeta_5$ has degree $4$ over $\mathbb{Q}$ and $\zeta_7$ has degree $6$ over $\mathbb{Q}$

Published on 25 Mar 2026 - 23:52

score 127 · Answer 5 · 2026-03-25 22:23:49

127

Views

How to factor this polynomial over $\mathbb{F}_2$

Published on 25 Mar 2026 - 22:23

score 389 · Answer 6 · 2026-03-19 22:24:01

389

Views

Finite dimensional central division $\mathbb K$-algebra as a subalgebra of a matrix $\mathbb K$-algebra

Published on 19 Mar 2026 - 22:24

score 1.8k · Answer 7 · 2018-04-06 22:14:45

1.8k

Views

Non-distributive fields?

Published on 06 Apr 2018 - 22:14

score 125 · Answer 8 · 2026-03-25 22:25:12

125

Views

Can Wedderburn's theorem proof be given by integral domain argument directly?

Published on 25 Mar 2026 - 22:25

score 450 · Answer 9 · 2026-03-27 04:23:54

450

Views

The Galois group of $x^{4}-a$ over $\mathbb{Q}$ where $a$ is any integer $\neq 0$, $\neq \pm 1$ and is square free.

Published on 27 Mar 2026 - 4:23

score 459 · Answer 10 · 2018-04-07 18:39:39

459

Views

Field inclusion

Published on 07 Apr 2018 - 18:39

score 41 · Answer 11 · 2026-03-25 12:22:38

41

Views

Examples in finite extensions.

Published on 25 Mar 2026 - 12:22

score 480 · Answer 12 · 2026-03-27 04:23:54

480

Views

Find the Galois group of $x^{4}-t$ over $\mathbb{R}(t)$, where $t$ is transcendental over the complex number $\mathbb{C}$

Published on 27 Mar 2026 - 4:23

score 86 · Answer 13 · 2026-03-25 22:26:52

86

Views

If $a$ and $b$ are elements of a finite field $k$, then $f(x)$ must have a root in $k$

Published on 25 Mar 2026 - 22:26

score 106 · Answer 14 · 2026-03-25 09:24:28

106

Views

Characteristic $0$ non-algebraically closed field which does not admit an ordering

Published on 25 Mar 2026 - 9:24

score 35 · Answer 15 · 2018-04-08 18:00:23

35

Views

The equivalent conditions for a subset of a field being a subspace

Published on 08 Apr 2018 - 18:00

List Question

Factorization on an arbitrary field

Proof that $[\overline{\mathbb Q}:\mathbb R\cap\overline{\mathbb Q}]=2$

prove that if $a=b$ then $a+c=b+c$ where $a,b,c\in \mathbb R$

$\zeta_5$ has degree $4$ over $\mathbb{Q}$ and $\zeta_7$ has degree $6$ over $\mathbb{Q}$

How to factor this polynomial over $\mathbb{F}_2$

Finite dimensional central division $\mathbb K$-algebra as a subalgebra of a matrix $\mathbb K$-algebra

Non-distributive fields?

Can Wedderburn's theorem proof be given by integral domain argument directly?

The Galois group of $x^{4}-a$ over $\mathbb{Q}$ where $a$ is any integer $\neq 0$, $\neq \pm 1$ and is square free.

Field inclusion

Examples in finite extensions.

Find the Galois group of $x^{4}-t$ over $\mathbb{R}(t)$, where $t$ is transcendental over the complex number $\mathbb{C}$

If $a$ and $b$ are elements of a finite field $k$, then $f(x)$ must have a root in $k$

Characteristic $0$ non-algebraically closed field which does not admit an ordering

The equivalent conditions for a subset of a field being a subspace

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