Question

Is $\alpha \in \mathbb{F}_{p^n}$ separable over $\mathbb{F}_p(t)$?

score 42 · Answer 1 · 2026-04-09 17:13:15

42

Views

Is $\alpha \in \mathbb{F}_{p^n}$ separable over $\mathbb{F}_p(t)$?

Published on 09 Apr 2026 - 17:13

score 36 · Answer 2 · 2026-04-15 00:30:33

36

Views

Show that the intersection of all subfields is the prime field

Published on 15 Apr 2026 - 0:30

score 55 · Answer 3 · 2026-04-16 07:41:49

55

Views

Irreducibility over $\mathbb{Q}(\sqrt[19]{2})$

Published on 16 Apr 2026 - 7:41

score 121 · Answer 4 · 2026-04-13 17:49:22

121

Views

why is this elementary linear algebra proof wrong?

Published on 13 Apr 2026 - 17:49

score 83 · Answer 5 · 2026-04-16 12:11:25

83

Views

Inner product on $\mathbb{Q}$

Published on 16 Apr 2026 - 12:11

score 79 · Answer 6 · 2026-04-10 00:06:32

79

Views

Proof verification (Galois Theory): Embeddings of finite separable extension into algebraic closure

Published on 10 Apr 2026 - 0:06

score 91 · Answer 7 · 2026-04-16 17:28:38

91

Views

Solvable extension is solvable by radicals

Published on 16 Apr 2026 - 17:28

score 98 · Answer 8 · 2026-04-15 07:39:58

98

Views

Find the splitting field of $F = \{ x^{4}+1,x^{5}+2\}$ over $\mathbb Q$ and its extension-degree

Published on 15 Apr 2026 - 7:39

score 64 · Answer 9 · 2026-04-15 10:32:02

64

Views

Let $K_1, K_2$ be fields and $f: K_1 \to K_2$ Ring Homomorphism. Prove $f$ is injective or Zero Homomorphism ($f(a) = 0_{K_2}$ for all $a \in K_1$)

Published on 15 Apr 2026 - 10:32

score 98 · Answer 10 · 2026-04-14 15:55:50

98

Views

$X^p - a$ is irreducible (Example 2.3 from Milne's Field Theory)

Published on 14 Apr 2026 - 15:55

score 421 · Answer 11 · 2026-04-14 16:51:50

421

Views

When is $\mathbb{F}_{p^k}^{\times} \cong \mathbb{Z}_m^{\times}$ for $k>1$?

Published on 14 Apr 2026 - 16:51

score 38 · Answer 12 · 2026-03-25 20:58:02

38

Views

Artin's theorem in the infinite dimensional case

Published on 25 Mar 2026 - 20:58

score 108 · Answer 13 · 2026-05-11 01:47:12

108

Views

Isomorphisms between sub division rings of degree $2$

Published on 11 May 2026 - 1:47

score 50 · Answer 14 · 2026-04-12 06:29:11

50

Views

Defining discriminants in Grothendieck's Galois theory

Published on 12 Apr 2026 - 6:29

score 56 · Answer 15 · 2026-04-14 19:43:30

56

Views

Describe the embeddings of L extending σ1, and the embeddings of L extending σ2. Which are real and which are complex? What is the signature of L?

Published on 14 Apr 2026 - 19:43

List Question

Is $\alpha \in \mathbb{F}_{p^n}$ separable over $\mathbb{F}_p(t)$?

Show that the intersection of all subfields is the prime field

Irreducibility over $\mathbb{Q}(\sqrt[19]{2})$

why is this elementary linear algebra proof wrong?

Inner product on $\mathbb{Q}$

Proof verification (Galois Theory): Embeddings of finite separable extension into algebraic closure

Solvable extension is solvable by radicals

Find the splitting field of $F = \{ x^{4}+1,x^{5}+2\}$ over $\mathbb Q$ and its extension-degree

Let $K_1, K_2$ be fields and $f: K_1 \to K_2$ Ring Homomorphism. Prove $f$ is injective or Zero Homomorphism ($f(a) = 0_{K_2}$ for all $a \in K_1$)

$X^p - a$ is irreducible (Example 2.3 from Milne's Field Theory)

When is $\mathbb{F}_{p^k}^{\times} \cong \mathbb{Z}_m^{\times}$ for $k>1$?

Artin's theorem in the infinite dimensional case

Isomorphisms between sub division rings of degree $2$

Defining discriminants in Grothendieck's Galois theory

Describe the embeddings of L extending σ1, and the embeddings of L extending σ2. Which are real and which are complex? What is the signature of L?

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