List questions from field-theory

Published on 25 Mar 2026 - 17:51

60

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Finite field as $F_p$ vector space

Published on 17 Apr 2026 - 1:36

83

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Finite separable field extension of a non-perfect field $K$ of characteristic $p > 0$ that has degree divisible by $p$.

Published on 09 Apr 2026 - 17:15

75

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What are the advantages of separable extensions?

Published on 11 Apr 2026 - 8:59

89

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What is the Galois group of $\bar{\mathbb{Q}}/\mathbb{Q}$?

Published on 14 Apr 2026 - 9:40

90

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On a particular way to compare fields

Published on 13 Apr 2026 - 16:34

89

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$-1$ is not a square in $\mathbb F_p$ if $p$ is congruent to $3$ modulo $4$

Published on 16 Apr 2026 - 1:05

27

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Degree of extension of $\mathbb Q(\sqrt{a_1},\cdots,\sqrt{a_n})$ over $\mathbb Q$

Published on 17 Apr 2026 - 9:43

70

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Galois group of splitting field over an infinite field of prime characteristic

Published on 12 Apr 2026 - 7:16

154

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Representing finite fields

Published on 16 Apr 2026 - 8:58

78

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When do the eigenvalues of a symmetric matrix belong to its field?

Published on 11 Apr 2026 - 6:08

68

Views

Algebraically closed field s.t. $K\simeq L$, $K\subsetneq L$.

Published on 15 Apr 2026 - 4:10

113

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Proof that {1, pi} generates the extension R/Q

Published on 15 Apr 2026 - 2:30

73

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understanding the proof of Krull theorem on topological groups

Published on 09 Apr 2026 - 5:49

133

Views

Degree of $F(\alpha, \beta)$ over $F(\alpha + \beta)$

Published on 15 Apr 2026 - 17:32

List Question

Same field extension, different irreducible polynomial?

Finite field as $F_p$ vector space

Finite separable field extension of a non-perfect field $K$ of characteristic $p > 0$ that has degree divisible by $p$.

What are the advantages of separable extensions?

What is the Galois group of $\bar{\mathbb{Q}}/\mathbb{Q}$?

On a particular way to compare fields

$-1$ is not a square in $\mathbb F_p$ if $p$ is congruent to $3$ modulo $4$

Degree of extension of $\mathbb Q(\sqrt{a_1},\cdots,\sqrt{a_n})$ over $\mathbb Q$

Galois group of splitting field over an infinite field of prime characteristic

Representing finite fields

When do the eigenvalues of a symmetric matrix belong to its field?

Algebraically closed field s.t. $K\simeq L$, $K\subsetneq L$.

Proof that {1, pi} generates the extension R/Q

understanding the proof of Krull theorem on topological groups

Degree of $F(\alpha, \beta)$ over $F(\alpha + \beta)$

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