Question

What is the value of $[K : \Bbb F_p]$?

score 75 · Answer 1 · 2026-04-15 15:34:51

75

Views

What is the value of $[K : \Bbb F_p]$?

Published on 15 Apr 2026 - 15:34

score 331 · Answer 2 · 2026-04-13 17:37:46

331

Views

Galois Group of splitting field of $ X^5 - 4X + 6 $ over $\mathbb{Q}$

Published on 13 Apr 2026 - 17:37

score 182 · Answer 3 · 2026-04-12 23:40:09

182

Views

Find a splitting field extension for $t^3-5$ over $\mathbb{Z}_7$, $\mathbb{Z}_{11}$, and $\mathbb{Z}_{13}$

Published on 12 Apr 2026 - 23:40

score 135 · Answer 4 · 2026-04-14 22:50:51

135

Views

Suppose $M : L$ and $L : K$ are extensions, and that $\alpha \in M$ is algebraic over $K$. Does $[L(\alpha):L]$ always divide $[K(\alpha):K]$?

Published on 14 Apr 2026 - 22:50

score 179 · Answer 5 · 2026-04-13 08:25:45

179

Views

Radical extension and characteristic of underlying field

Published on 13 Apr 2026 - 8:25

score 115 · Answer 6 · 2026-04-17 03:56:19

115

Views

Show that $\lvert \mathbb{Q}(\sqrt2 , \sqrt{1+i}) : \mathbb{Q} \rvert = 8$

Published on 17 Apr 2026 - 3:56

score 176 · Answer 7 · 2026-04-12 16:53:57

176

Views

Prove that $1_R=1_K$

Published on 12 Apr 2026 - 16:53

score 135 · Answer 8 · 2026-04-16 13:39:59

135

Views

$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$

Published on 16 Apr 2026 - 13:39

score 30 · Answer 9 · 2026-04-16 12:56:27

30

Views

Solving 2 equations for a field

Published on 16 Apr 2026 - 12:56

score 1.3k · Answer 10 · 2026-04-15 20:28:04

1.3k

Views

Prove that $x^4+15x^3+7$ is irreducible over $ \mathbb Q$?

Published on 15 Apr 2026 - 20:28

score 257 · Answer 11 · 2026-04-12 08:26:36

257

Views

Dimension of division ring over center cannot be prime

Published on 12 Apr 2026 - 8:26

score 40 · Answer 12 · 2026-04-15 12:40:09

let $E$ be a splitting field of $p(x)$ the minimal polynomial of $u$ over $K$ then $E \subset F$ where $F=K(u)$ is normal over K, $u \in F$

score 248 · Answer 13 · 2026-04-12 02:48:19

248

Views

Algebraic closure of a field $K$ actually containing $K$ as a subset

Published on 12 Apr 2026 - 2:48

score 24 · Answer 14 · 2026-04-14 01:21:18

24

Views

Prove inequality with multiple variables in a field

Published on 14 Apr 2026 - 1:21

score 65 · Answer 15 · 2026-04-11 07:26:59

65

Views

Final theorem of arithmetic

Published on 11 Apr 2026 - 7:26

List Question

What is the value of $[K : \Bbb F_p]$?

Galois Group of splitting field of $ X^5 - 4X + 6 $ over $\mathbb{Q}$

Find a splitting field extension for $t^3-5$ over $\mathbb{Z}_7$, $\mathbb{Z}_{11}$, and $\mathbb{Z}_{13}$

Suppose $M : L$ and $L : K$ are extensions, and that $\alpha \in M$ is algebraic over $K$. Does $[L(\alpha):L]$ always divide $[K(\alpha):K]$?

Radical extension and characteristic of underlying field

Show that $\lvert \mathbb{Q}(\sqrt2 , \sqrt{1+i}) : \mathbb{Q} \rvert = 8$

Prove that $1_R=1_K$

$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$

Solving 2 equations for a field

Prove that $x^4+15x^3+7$ is irreducible over $ \mathbb Q$?

Dimension of division ring over center cannot be prime

let $E$ be a splitting field of $p(x)$ the minimal polynomial of $u$ over $K$ then $E \subset F$ where $F=K(u)$ is normal over K, $u \in F$

Algebraic closure of a field $K$ actually containing $K$ as a subset

Prove inequality with multiple variables in a field

Final theorem of arithmetic

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