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Galois Theory: Increasing sequence of Fields corresponds to decreasing sequence of subgroups

score 66 · Answer 1 · 2026-04-11 16:25:46

66

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Galois Theory: Increasing sequence of Fields corresponds to decreasing sequence of subgroups

Published on 11 Apr 2026 - 16:25

score 339 · Answer 2 · 2026-04-12 08:01:13

339

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Extension of ideals in polynomial ring extension

Published on 12 Apr 2026 - 8:01

score 186 · Answer 3 · 2026-04-11 14:58:34

186

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Galois Theory: Are separable and normal equivalent?

Published on 11 Apr 2026 - 14:58

score 1.4k · Answer 4 · 2026-04-15 12:05:11

Field extensions $F \subset K \subset L$, $a \in L$ is algebraic over $K$, and $K$ is algebraic over $F$, then $a$ is algebraic over $F$.

score 1.1k · Answer 5 · 2026-04-15 15:17:39

1.1k

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Let $F,K$ be fields, prove that any element in $K$ that is not in $F$ is irreducible in $F[x]$ of degree $p$.

Published on 15 Apr 2026 - 15:17

score 1k · Answer 6 · 2026-04-14 00:56:14

1k

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Degree of a field extension over $\mathbb Q$.

Published on 14 Apr 2026 - 0:56

score 37 · Answer 7 · 2026-04-23 15:02:52

37

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clarification for a field extension argument

Published on 23 Apr 2026 - 15:02

score 537 · Answer 8 · 2026-04-11 23:05:43

537

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About primes and cyclotomic extensions

Published on 11 Apr 2026 - 23:05

score 177 · Answer 9 · 2026-04-13 06:06:53

177

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How to prove an element belongs to a splitting field?

Published on 13 Apr 2026 - 6:06

score 59 · Answer 10 · 2026-04-15 14:14:32

59

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$k \subset L_i \subset M$ with $k \subset L_i$ and $k \subset M$ transcendental of the same degree

Published on 15 Apr 2026 - 14:14

score 69 · Answer 11 · 2026-04-15 00:09:11

69

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Question about vector space representation of field extension $\mathbb{Q(\sqrt[3]{2},\zeta)}$

Published on 15 Apr 2026 - 0:09

score 58 · Answer 12 · 2026-04-23 20:10:37

58

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Elements in an extension of a finite field $\mathbb{F}_p$.

Published on 23 Apr 2026 - 20:10

score 292 · Answer 13 · 2026-04-12 10:46:23

292

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Finding GCD of two elements over a quadratic extension of integers

Published on 12 Apr 2026 - 10:46

score 272 · Answer 14 · 2026-04-15 19:55:28

272

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Find the degree of $K = \mathbb{Q}(\sqrt2, \sqrt7)$ over $\mathbb{Q}$

Published on 15 Apr 2026 - 19:55

score 1k · Answer 15 · 2026-04-14 04:32:58

1k

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the Galois group of $x^5-1$ over the rational numbers

Published on 14 Apr 2026 - 4:32

List Question

Galois Theory: Increasing sequence of Fields corresponds to decreasing sequence of subgroups

Extension of ideals in polynomial ring extension

Galois Theory: Are separable and normal equivalent?

Field extensions $F \subset K \subset L$, $a \in L$ is algebraic over $K$, and $K$ is algebraic over $F$, then $a$ is algebraic over $F$.

Let $F,K$ be fields, prove that any element in $K$ that is not in $F$ is irreducible in $F[x]$ of degree $p$.

Degree of a field extension over $\mathbb Q$.

clarification for a field extension argument

About primes and cyclotomic extensions

How to prove an element belongs to a splitting field?

$k \subset L_i \subset M$ with $k \subset L_i$ and $k \subset M$ transcendental of the same degree

Question about vector space representation of field extension $\mathbb{Q(\sqrt[3]{2},\zeta)}$

Elements in an extension of a finite field $\mathbb{F}_p$.

Finding GCD of two elements over a quadratic extension of integers

Find the degree of $K = \mathbb{Q}(\sqrt2, \sqrt7)$ over $\mathbb{Q}$

the Galois group of $x^5-1$ over the rational numbers

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