Question

$E_1/F$ and $E_2/F$ finite field extensions, does degree of compositum $E_1E_2$ over $F$ divide the product $[E_1:F] [E_2:F]$?

score 881 · Answer 1 · 2020-05-06 17:33:04

881

Views

$E_1/F$ and $E_2/F$ finite field extensions, does degree of compositum $E_1E_2$ over $F$ divide the product $[E_1:F] [E_2:F]$?

Published on 06 May 2020 - 17:33

score 593 · Answer 2 · 2026-02-23 06:38:05

593

Views

Degree of separability equals degree of separable closure

Published on 23 Feb 2026 - 6:38

score 67 · Answer 3 · 2020-05-07 08:07:22

67

Views

The number of intermediate field extensions $\mathbb{Q}(ζ_{630})/M/\mathbb{Q}$ of $[M:Q]=3$

Published on 07 May 2020 - 8:07

score 22 · Answer 4 · 2020-05-08 09:49:07

22

Views

How are these two lemmas about simple algebraic extensions and polynomials restatements of each other?

Published on 08 May 2020 - 9:49

score 110 · Answer 5 · 2020-05-09 12:42:00

110

Views

Field extension of degree three

Published on 09 May 2020 - 12:42

score 94 · Answer 6 · 2020-05-09 14:55:00

94

Views

Calculate the degree $[K:\mathbb{Q}]$

Published on 09 May 2020 - 14:55

score 88 · Answer 7 · 2026-03-26 09:26:55

88

Views

Valuation ring, containing a Noetherian local domain, whose fraction field is a finite extension of that of the Noetherian domain

Published on 26 Mar 2026 - 9:26

score 190 · Answer 8 · 2026-03-28 18:15:59

190

Views

Linearly independent vectors over a field and its subfield

Published on 28 Mar 2026 - 18:15

score 157 · Answer 9 · 2026-03-26 17:50:20

157

Views

Can there exist a finite extension $K$ where $K$ is Galois over $\mathbb Q(i)$ but $K$ is not Galois over $\mathbb Q?$

Published on 26 Mar 2026 - 17:50

score 133 · Answer 10 · 2026-03-27 13:49:38

133

Views

On a special kind of Discrete Valuation Ring

Published on 27 Mar 2026 - 13:49

score 48 · Answer 11 · 2020-05-15 03:36:29

48

Views

If $K=\{a+b\sqrt2\mid a,b\in\mathbb{Q}\}$, find $[K ∶\mathbb{Q}]$ and $[K(\sqrt3) ∶\mathbb{Q}]$.

Published on 15 May 2020 - 3:36

score 150 · Answer 12 · 2020-05-15 09:26:09

150

Views

Calculate the degree of a composite field extension

Published on 15 May 2020 - 9:26

score 456 · Answer 13 · 2026-03-28 06:13:26

456

Views

Galois Group of $x^{6}-2x^{3}-1$

Published on 28 Mar 2026 - 6:13

score 86 · Answer 14 · 2020-05-17 13:31:01

86

Views

Is every field a field extension of some form.

Published on 17 May 2020 - 13:31

score 194 · Answer 15 · 2020-05-18 14:16:23

194

Views

Show that a field extension is a radical extension

Published on 18 May 2020 - 14:16

List Question

$E_1/F$ and $E_2/F$ finite field extensions, does degree of compositum $E_1E_2$ over $F$ divide the product $[E_1:F] [E_2:F]$?

Degree of separability equals degree of separable closure

The number of intermediate field extensions $\mathbb{Q}(ζ_{630})/M/\mathbb{Q}$ of $[M:Q]=3$

How are these two lemmas about simple algebraic extensions and polynomials restatements of each other?

Field extension of degree three

Calculate the degree $[K:\mathbb{Q}]$

Valuation ring, containing a Noetherian local domain, whose fraction field is a finite extension of that of the Noetherian domain

Linearly independent vectors over a field and its subfield

Can there exist a finite extension $K$ where $K$ is Galois over $\mathbb Q(i)$ but $K$ is not Galois over $\mathbb Q?$

On a special kind of Discrete Valuation Ring

If $K=\{a+b\sqrt2\mid a,b\in\mathbb{Q}\}$, find $[K ∶\mathbb{Q}]$ and $[K(\sqrt3) ∶\mathbb{Q}]$.

Calculate the degree of a composite field extension

Galois Group of $x^{6}-2x^{3}-1$

Is every field a field extension of some form.

Show that a field extension is a radical extension

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