Question

Prove that $[\mathbb{Q}(\sqrt[4]{2}, \sqrt{3}):\mathbb{Q}] = 8$

score 110 · Answer 1 · 2026-04-17 06:17:18

110

Views

Prove that $[\mathbb{Q}(\sqrt[4]{2}, \sqrt{3}):\mathbb{Q}] = 8$

Published on 17 Apr 2026 - 6:17

score 32 · Answer 2 · 2026-04-15 16:13:20

32

Views

Expression of singlets in multiplication of simple Lie group Representations.

Published on 15 Apr 2026 - 16:13

score 65 · Answer 3 · 2026-04-17 06:32:18

For coprime integers $p,q>0$ and $u,v$ real numbers algebraic over $\mathbb{Q}$ of degrees $p$ & $q$, prove $[\mathbb{Q}(u,v) : \mathbb{Q}] = pq$

score 130 · Answer 4 · 2026-04-15 19:32:55

130

Views

Show this element is in the center of the group?

Published on 15 Apr 2026 - 19:32

score 838 · Answer 5 · 2026-04-15 18:46:08

838

Views

If $A$ is idempotent then $A$ is similar to a diagonal matrix with only $0$'s and $1$'s on the diagonal.

Published on 15 Apr 2026 - 18:46

score 70 · Answer 6 · 2026-04-14 17:51:16

70

Views

How to manipulate matrices whose elements are themselves matrices or other unique entities?

Published on 14 Apr 2026 - 17:51

score 488 · Answer 7 · 2026-04-14 06:27:29

488

Views

Apply Lam's theorem to determine all the left ideals of $\begin{pmatrix}\mathbb{Q}&\mathbb{R}\\0&\mathbb{R}\end{pmatrix}$

Published on 14 Apr 2026 - 6:27

score 108 · Answer 8 · 2026-04-13 09:58:22

108

Views

Composite of field extensions

Published on 13 Apr 2026 - 9:58

score 295 · Answer 9 · 2026-04-17 01:26:35

295

Views

Proving the lemma $\sqrt2\notin\mathbb{Q}(\sqrt3,\sqrt5)$

Published on 17 Apr 2026 - 1:26

score 228 · Answer 10 · 2026-04-11 11:51:04

228

Views

$PSL_2(\mathbb{Z})$ is isomorphic to $\mathbb{Z}_2 \ast \mathbb{Z}_3$

Published on 11 Apr 2026 - 11:51

score 37 · Answer 11 · 2026-04-01 12:33:48

37

Views

Factorization on an arbitrary field

Published on 01 Apr 2026 - 12:33

score 3.4k · Answer 12 · 2026-04-13 20:11:07

3.4k

Views

Prove the intersection of two prime ideals is prime if and only if one is a subset of the other?

Published on 13 Apr 2026 - 20:11

score 589 · Answer 13 · 2026-04-14 03:42:06

589

Views

Abstract Algebra: The set of homomorphisms between two free modules is a free module.

Published on 14 Apr 2026 - 3:42

score 93 · Answer 14 · 2026-04-14 05:39:54

93

Views

Let $H = \{e, (12)\} \subset S_3$. Find the orbit of $H$ under conjugation by $G$.

Published on 14 Apr 2026 - 5:39

score 163 · Answer 15 · 2026-04-16 16:10:57

163

Views

Proof that $[\overline{\mathbb Q}:\mathbb R\cap\overline{\mathbb Q}]=2$

Published on 16 Apr 2026 - 16:10

List Question

Prove that $[\mathbb{Q}(\sqrt[4]{2}, \sqrt{3}):\mathbb{Q}] = 8$

Expression of singlets in multiplication of simple Lie group Representations.

For coprime integers $p,q>0$ and $u,v$ real numbers algebraic over $\mathbb{Q}$ of degrees $p$ & $q$, prove $[\mathbb{Q}(u,v) : \mathbb{Q}] = pq$

Show this element is in the center of the group?

If $A$ is idempotent then $A$ is similar to a diagonal matrix with only $0$'s and $1$'s on the diagonal.

How to manipulate matrices whose elements are themselves matrices or other unique entities?

Apply Lam's theorem to determine all the left ideals of $\begin{pmatrix}\mathbb{Q}&\mathbb{R}\\0&\mathbb{R}\end{pmatrix}$

Composite of field extensions

Proving the lemma $\sqrt2\notin\mathbb{Q}(\sqrt3,\sqrt5)$

$PSL_2(\mathbb{Z})$ is isomorphic to $\mathbb{Z}_2 \ast \mathbb{Z}_3$

Factorization on an arbitrary field

Prove the intersection of two prime ideals is prime if and only if one is a subset of the other?

Abstract Algebra: The set of homomorphisms between two free modules is a free module.

Let $H = \{e, (12)\} \subset S_3$. Find the orbit of $H$ under conjugation by $G$.

Proof that $[\overline{\mathbb Q}:\mathbb R\cap\overline{\mathbb Q}]=2$

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