Question

isomorphism between a field and non-field rings

score 186 · Answer 1 · 2026-04-13 09:56:09

186

Views

isomorphism between a field and non-field rings

Published on 13 Apr 2026 - 9:56

score 99 · Answer 2 · 2026-04-14 14:38:18

99

Views

Understanding the proof of: $p$ is prime and $a \in \mathbb{Z}_p \implies x^p - a \in \mathbb{Z}_p$ is reducible.

Published on 14 Apr 2026 - 14:38

score 66 · Answer 3 · 2026-03-25 18:55:05

66

Views

Checking if the intersection of two cyclic $p$-adic extensions with certain properties is trivial

Published on 25 Mar 2026 - 18:55

score 75 · Answer 4 · 2026-04-09 10:05:41

75

Views

equivalent condition for a quadratic number field to have a solution of the equation $x^2+y^2=-1$

Published on 09 Apr 2026 - 10:05

score 2.5k · Answer 5 · 2026-04-13 23:59:47

2.5k

Views

A field is a commutative division ring

Published on 13 Apr 2026 - 23:59

score 176 · Answer 6 · 2026-03-26 08:03:36

176

Views

Is an integral domain $\frac{\mathbb{C}[x,y]}{<x^4+x^3y+y^4>}$?

Published on 26 Mar 2026 - 8:03

score 103 · Answer 7 · 2026-03-29 03:36:38

103

Views

Let $X = \{ \sqrt{p} : p \text{ is prime} \}$, $Y \subseteq X$ and $\sqrt{p} \not\in Y$. Show that $[\mathbb{Q}(Y)(\sqrt{p}) : \mathbb{Q}(Y)] = 2$.

Published on 29 Mar 2026 - 3:36

score 117 · Answer 8 · 2026-04-08 22:07:05

117

Views

Two candidates for definition of splitting field

Published on 08 Apr 2026 - 22:07

score 63 · Answer 9 · 2026-04-12 05:06:21

63

Views

Ordered field in convex subset definition

Published on 12 Apr 2026 - 5:06

score 152 · Answer 10 · 2026-04-15 06:17:10

152

Views

Find a splitting field and its Galois group

Published on 15 Apr 2026 - 6:17

score 52 · Answer 11 · 2026-04-16 21:25:34

52

Views

Use $\alpha$ to write a basis for $K$ over $F$

Published on 16 Apr 2026 - 21:25

score 48 · Answer 12 · 2026-04-13 20:08:36

48

Views

Prove that solution of equation $x^p=a$ exists, where $a$ is a fixed element in a finite field $F$ and $charF=p.$

Published on 13 Apr 2026 - 20:08

score 102 · Answer 13 · 2026-04-14 05:24:12

102

Views

Irreducible polynomial in field extension (alternative proof)

Published on 14 Apr 2026 - 5:24

score 61 · Answer 14 · 2026-04-15 11:02:58

61

Views

Polynomial over $\Bbb Q$ implies transitivity of the action of its Galois group

Published on 15 Apr 2026 - 11:02

score 64 · Answer 15 · 2026-04-14 01:28:33

64

Views

Is the following a correct proof that $t^4-32$ is irreducible over $\mathbb{Z}$?

Published on 14 Apr 2026 - 1:28

List Question

isomorphism between a field and non-field rings

Understanding the proof of: $p$ is prime and $a \in \mathbb{Z}_p \implies x^p - a \in \mathbb{Z}_p$ is reducible.

Checking if the intersection of two cyclic $p$-adic extensions with certain properties is trivial

equivalent condition for a quadratic number field to have a solution of the equation $x^2+y^2=-1$

A field is a commutative division ring

Is an integral domain $\frac{\mathbb{C}[x,y]}{<x^4+x^3y+y^4>}$?

Let $X = \{ \sqrt{p} : p \text{ is prime} \}$, $Y \subseteq X$ and $\sqrt{p} \not\in Y$. Show that $[\mathbb{Q}(Y)(\sqrt{p}) : \mathbb{Q}(Y)] = 2$.

Two candidates for definition of splitting field

Ordered field in convex subset definition

Find a splitting field and its Galois group

Use $\alpha$ to write a basis for $K$ over $F$

Prove that solution of equation $x^p=a$ exists, where $a$ is a fixed element in a finite field $F$ and $charF=p.$

Irreducible polynomial in field extension (alternative proof)

Polynomial over $\Bbb Q$ implies transitivity of the action of its Galois group

Is the following a correct proof that $t^4-32$ is irreducible over $\mathbb{Z}$?

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