Question

If every intermediate ring of a field extension is a field, then the extension is algebraic

score 1.6k · Answer 1 · 2026-04-14 06:21:52

1.6k

Views

If every intermediate ring of a field extension is a field, then the extension is algebraic

Published on 14 Apr 2026 - 6:21

score 22 · Answer 2 · 2026-04-12 16:34:47

22

Views

On the question of the Galois group of some polynomial.

Published on 12 Apr 2026 - 16:34

score 44 · Answer 3 · 2026-04-11 16:48:20

44

Views

The simplest reference for Wedderburn decomposition

Published on 11 Apr 2026 - 16:48

score 60 · Answer 4 · 2026-04-15 06:16:24

60

Views

Showing that this polynomial is in F[x] (Galois theory, given K is some extension of F)

Published on 15 Apr 2026 - 6:16

score 129 · Answer 5 · 2026-04-11 13:21:56

129

Views

Explicit matrix representation of an algebraic extension

Published on 11 Apr 2026 - 13:21

score 132 · Answer 6 · 2026-04-12 12:40:08

132

Views

Field extension if element fixed by only identity

Published on 12 Apr 2026 - 12:40

score 80 · Answer 7 · 2026-04-12 04:25:49

80

Views

polynomial in fixed field

Published on 12 Apr 2026 - 4:25

score 142 · Answer 8 · 2026-04-15 13:27:02

142

Views

Showing that the multiplicative group of roots of $x^n - 1$ in $\overline{F}$ has $\phi(n)$ distinct generators

Published on 15 Apr 2026 - 13:27

score 116 · Answer 9 · 2026-04-11 18:02:22

116

Views

Given a tower of field extensions, does this equality involving Galois group orders hold in general?

Published on 11 Apr 2026 - 18:02

score 485 · Answer 10 · 2026-04-16 07:09:33

485

Views

How is $Gal(\mathbb{Q}(\sqrt[4]{3}, i)$ equal to $D_8$? (dihedral group of order 8)

Published on 16 Apr 2026 - 7:09

score 90 · Answer 11 · 2026-04-13 06:53:22

90

Views

Showing that the group of $n^{th}$ roots of unity form a group

Published on 13 Apr 2026 - 6:53

score 986 · Answer 12 · 2026-04-14 08:32:13

986

Views

Showing normalizer of Galois group

Published on 14 Apr 2026 - 8:32

score 124 · Answer 13 · 2026-04-16 03:12:50

124

Views

No $p$-th root implies $X^{p^n}-a$ irreducible for all $n \in \mathbb{N}$

Published on 16 Apr 2026 - 3:12

score 149 · Answer 14 · 2026-04-15 15:43:01

149

Views

Field theory: an equality involving the number of homomorphisms from an extension $E$ of $F$ to $\overline{F}$

Published on 15 Apr 2026 - 15:43

score 480 · Answer 15 · 2026-04-17 06:13:36

480

Views

Degree of a finite field extension

Published on 17 Apr 2026 - 6:13

List Question

If every intermediate ring of a field extension is a field, then the extension is algebraic

On the question of the Galois group of some polynomial.

The simplest reference for Wedderburn decomposition

Showing that this polynomial is in F[x] (Galois theory, given K is some extension of F)

Explicit matrix representation of an algebraic extension

Field extension if element fixed by only identity

polynomial in fixed field

Showing that the multiplicative group of roots of $x^n - 1$ in $\overline{F}$ has $\phi(n)$ distinct generators

Given a tower of field extensions, does this equality involving Galois group orders hold in general?

How is $Gal(\mathbb{Q}(\sqrt[4]{3}, i)$ equal to $D_8$? (dihedral group of order 8)

Showing that the group of $n^{th}$ roots of unity form a group

Showing normalizer of Galois group

No $p$-th root implies $X^{p^n}-a$ irreducible for all $n \in \mathbb{N}$

Field theory: an equality involving the number of homomorphisms from an extension $E$ of $F$ to $\overline{F}$

Degree of a finite field extension

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