Question

Rupture field of an irreducible polynomial over a finite field equals its splitting field

score 69 · Answer 1 · 2026-04-12 22:49:40

69

Views

Rupture field of an irreducible polynomial over a finite field equals its splitting field

Published on 12 Apr 2026 - 22:49

score 76 · Answer 2 · 2026-04-14 03:40:57

76

Views

If $K$ is algebraically closed, is the fixed field of an involution real-closed?

Published on 14 Apr 2026 - 3:40

score 201 · Answer 3 · 2026-04-14 07:03:19

201

Views

Deduce the degree of the extension $[\mathbb C:K]$ is countable and not finite

Published on 14 Apr 2026 - 7:03

score 47 · Answer 4 · 2026-04-11 16:13:10

47

Views

Is following a normal field extension?

Published on 11 Apr 2026 - 16:13

score 47 · Answer 5 · 2026-04-16 12:57:37

47

Views

Extensions with radicals such that $F=K_0\subseteq K_1\subseteq ... \subseteq K_m=K$ where every $[K_i:K_{i-1}]$ is a prime number

Published on 16 Apr 2026 - 12:57

score 143 · Answer 6 · 2026-04-16 13:58:26

143

Views

Fields and cubic extensions

Published on 16 Apr 2026 - 13:58

score 719 · Answer 7 · 2026-04-11 18:37:19

719

Views

Definition of pure transcendental extension

Published on 11 Apr 2026 - 18:37

score 78 · Answer 8 · 2026-04-13 18:29:13

78

Views

For $L/K$, is $\mathcal{O}_L$ the integral closure of $\mathcal{O}_K$

Published on 13 Apr 2026 - 18:29

score 41 · Answer 9 · 2026-04-13 14:08:08

41

Views

Homomorphism of fields

Published on 13 Apr 2026 - 14:08

score 72 · Answer 10 · 2026-04-14 23:47:53

72

Views

Question on why a field extension isn't a splitting field (and on general behavior of field extensions)

Published on 14 Apr 2026 - 23:47

score 49 · Answer 11 · 2026-04-12 02:12:00

49

Views

Given a proper field extension $L/K$, can we have $L\cong K$?

Published on 12 Apr 2026 - 2:12

score 56 · Answer 12 · 2026-04-13 16:41:46

56

Views

A question Monic Irreducible polynomial of $\sqrt{6}$ over $\mathbb{Q}(\sqrt{2},\sqrt{3})$

Published on 13 Apr 2026 - 16:41

score 39 · Answer 13 · 2026-04-16 03:43:23

39

Views

Understanding that $\mathbb{R}(X^2 + Y^2, XY)(x) \supset \mathbb{R}(Y)$?

Published on 16 Apr 2026 - 3:43

score 57 · Answer 14 · 2026-04-13 10:20:37

57

Views

Algebraic extensions and sub rings

Published on 13 Apr 2026 - 10:20

score 23 · Answer 15 · 2026-04-11 16:16:09

23

Views

Is the degree of a field extension inferiorly bounded by the degree of irreducible polynomials?

Published on 11 Apr 2026 - 16:16

List Question

Rupture field of an irreducible polynomial over a finite field equals its splitting field

If $K$ is algebraically closed, is the fixed field of an involution real-closed?

Deduce the degree of the extension $[\mathbb C:K]$ is countable and not finite

Is following a normal field extension?

Extensions with radicals such that $F=K_0\subseteq K_1\subseteq ... \subseteq K_m=K$ where every $[K_i:K_{i-1}]$ is a prime number

Fields and cubic extensions

Definition of pure transcendental extension

For $L/K$, is $\mathcal{O}_L$ the integral closure of $\mathcal{O}_K$

Homomorphism of fields

Question on why a field extension isn't a splitting field (and on general behavior of field extensions)

Given a proper field extension $L/K$, can we have $L\cong K$?

A question Monic Irreducible polynomial of $\sqrt{6}$ over $\mathbb{Q}(\sqrt{2},\sqrt{3})$

Understanding that $\mathbb{R}(X^2 + Y^2, XY)(x) \supset \mathbb{R}(Y)$?

Algebraic extensions and sub rings

Is the degree of a field extension inferiorly bounded by the degree of irreducible polynomials?

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