Question

Is $\mathbb{Q}(\sqrt 2,\sqrt 3,\sqrt 5)$ a simple extension?

score 5.9k · Answer 1 · 2026-04-16 13:20:59

5.9k

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Is $\mathbb{Q}(\sqrt 2,\sqrt 3,\sqrt 5)$ a simple extension?

Published on 16 Apr 2026 - 13:20

score 1.7k · Answer 2 · 2026-04-15 14:52:37

1.7k

Views

If the degree of field extension is a prime number, the extension is simple

Published on 15 Apr 2026 - 14:52

score 510 · Answer 3 · 2026-04-16 05:55:05

510

Views

When the extensions Q(α,β) and Q(αβ) over Q are the same?

Published on 16 Apr 2026 - 5:55

score 11.7k · Answer 4 · 2026-04-16 03:18:05

11.7k

Views

Similar matrices and field extensions

Published on 16 Apr 2026 - 3:18

score 682 · Answer 5 · 2026-04-13 08:39:49

682

Views

Degree of a field extension when compared to the Galois group

Published on 13 Apr 2026 - 8:39

score 11.2k · Answer 6 · 2026-04-17 13:48:55

11.2k

Views

Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.

Published on 17 Apr 2026 - 13:48

score 2.2k · Answer 7 · 2026-04-15 15:04:32

2.2k

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Subextension of a finitely generated extension of fields

Published on 15 Apr 2026 - 15:04

score 1.4k · Answer 8 · 2026-04-15 18:44:05

1.4k

Views

A basis for $k(X)$ regarded as a vector space over $k$

Published on 15 Apr 2026 - 18:44

score 692 · Answer 9 · 2026-04-13 12:40:47

692

Views

How to calculate separable closures of an algebraic extension?

Published on 13 Apr 2026 - 12:40

score 1.5k · Answer 10 · 2026-04-16 08:56:15

1.5k

Views

Hamel basis for $\mathbb{R}$ over $\mathbb{Q}$ cannot be closed under scalar multiplication by $a \ne 0,1$

Published on 16 Apr 2026 - 8:56

score 599 · Answer 11 · 2026-04-16 03:42:14

599

Views

Can we always find a primitive element that is a square?

Published on 16 Apr 2026 - 3:42

score 500 · Answer 12 · 2026-04-13 01:06:17

500

Views

Transcendental extension that is not simple

Published on 13 Apr 2026 - 1:06

score 688 · Answer 13 · 2026-04-12 03:32:01

688

Views

Finiteness of the Algebraic Closure

Published on 12 Apr 2026 - 3:32

score 1.2k · Answer 14 · 2026-04-15 07:24:28

1.2k

Views

Show that if $K \subset L$, then the separable closure of $K$ in $L$ is a field

Published on 15 Apr 2026 - 7:24

score 914 · Answer 15 · 2026-04-11 04:15:57

914

Views

If $K/F$ is a finite purely insep. extension, then there is a purely insep. extension of $K$ of degree $p$

Published on 11 Apr 2026 - 4:15

List Question

Is $\mathbb{Q}(\sqrt 2,\sqrt 3,\sqrt 5)$ a simple extension?

If the degree of field extension is a prime number, the extension is simple

When the extensions Q(α,β) and Q(αβ) over Q are the same?

Similar matrices and field extensions

Degree of a field extension when compared to the Galois group

Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.

Subextension of a finitely generated extension of fields

A basis for $k(X)$ regarded as a vector space over $k$

How to calculate separable closures of an algebraic extension?

Hamel basis for $\mathbb{R}$ over $\mathbb{Q}$ cannot be closed under scalar multiplication by $a \ne 0,1$

Can we always find a primitive element that is a square?

Transcendental extension that is not simple

Finiteness of the Algebraic Closure

Show that if $K \subset L$, then the separable closure of $K$ in $L$ is a field

If $K/F$ is a finite purely insep. extension, then there is a purely insep. extension of $K$ of degree $p$

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