Question

Galois group of $x^4-11$

score 150 · Answer 1 · 2026-04-14 05:38:29

150

Views

Galois group of $x^4-11$

Published on 14 Apr 2026 - 5:38

score 221 · Answer 2 · 2026-04-14 07:54:09

221

Views

Prove that $\mathbb{Q}(\sqrt{-5})$ has 2 roots of unity

Published on 14 Apr 2026 - 7:54

score 185 · Answer 3 · 2026-04-09 17:15:29

185

Views

If a real number can be expressed in terms of complex solutions of quintics, can it be expressed in terms of real solutions of quintics?

Published on 09 Apr 2026 - 17:15

score 95 · Answer 4 · 2026-04-15 10:18:32

95

Views

Is $\sqrt{5-2\sqrt{5}}$ in $\mathbb{Q}(\sqrt{5+2\sqrt{5}},\sqrt{2})$?

Published on 15 Apr 2026 - 10:18

score 246 · Answer 5 · 2026-04-16 07:24:28

246

Views

If $F$ is a finite field and $K$ is a subfield, then $F$ is isomorphic to $V_m(K) = \{(\lambda_1,...,\lambda_m)|\lambda_i \in K, i=1,2,...,m\}$

Published on 16 Apr 2026 - 7:24

score 89 · Answer 6 · 2026-04-13 04:17:29

89

Views

Is the intersection of all algebraically closed subextensions an algebraic closure?

Published on 13 Apr 2026 - 4:17

score 59 · Answer 7 · 2026-04-16 18:39:04

59

Views

Basis of $\mathbb{Q}(i, \sqrt{3})$ and minimal polynomials of $\sqrt{3}$ over $\mathbb{Q}$ and $i$ over $\mathbb{Q}(\sqrt{3}$)$

Published on 16 Apr 2026 - 18:39

score 28 · Answer 8 · 2026-04-15 06:16:42

28

Views

$x,y\in L$ tow algebraic element such that $xy,x+y\in K$. $x,y\in K$?

Published on 15 Apr 2026 - 6:16

score 50 · Answer 9 · 2026-04-17 01:18:46

50

Views

Difference Between Splitting Field of a Polynomial and Extension Field Generated by roots

Published on 17 Apr 2026 - 1:18

score 423 · Answer 10 · 2026-04-11 02:45:07

423

Views

Algebraic extension which is not finitely generated

Published on 11 Apr 2026 - 2:45

score 202 · Answer 11 · 2026-04-12 04:16:30

202

Views

seperability field extensions transitive

Published on 12 Apr 2026 - 4:16

score 30 · Answer 12 · 2026-04-13 13:06:11

30

Views

Point construction - one point equal to several points?

Published on 13 Apr 2026 - 13:06

score 112 · Answer 13 · 2026-04-14 20:30:06

112

Views

Prove the set of rational expressions $K(t)$ is a simple transcendental extension of the subfield $K$ of $\mathbb{C}$

Published on 14 Apr 2026 - 20:30

score 109 · Answer 14 · 2026-04-13 09:28:22

109

Views

Doubt about finite normal extensions: proof of the going-down theorem

Published on 13 Apr 2026 - 9:28

score 403 · Answer 15 · 2026-04-16 23:28:41

403

Views

Semisimple endomorphism: Equivalent definitions?

Published on 16 Apr 2026 - 23:28

List Question

Galois group of $x^4-11$

Prove that $\mathbb{Q}(\sqrt{-5})$ has 2 roots of unity

If a real number can be expressed in terms of complex solutions of quintics, can it be expressed in terms of real solutions of quintics?

Is $\sqrt{5-2\sqrt{5}}$ in $\mathbb{Q}(\sqrt{5+2\sqrt{5}},\sqrt{2})$?

If $F$ is a finite field and $K$ is a subfield, then $F$ is isomorphic to $V_m(K) = \{(\lambda_1,...,\lambda_m)|\lambda_i \in K, i=1,2,...,m\}$

Is the intersection of all algebraically closed subextensions an algebraic closure?

Basis of $\mathbb{Q}(i, \sqrt{3})$ and minimal polynomials of $\sqrt{3}$ over $\mathbb{Q}$ and $i$ over $\mathbb{Q}(\sqrt{3}$)$

$x,y\in L$ tow algebraic element such that $xy,x+y\in K$. $x,y\in K$?

Difference Between Splitting Field of a Polynomial and Extension Field Generated by roots

Algebraic extension which is not finitely generated

seperability field extensions transitive

Point construction - one point equal to several points?

Prove the set of rational expressions $K(t)$ is a simple transcendental extension of the subfield $K$ of $\mathbb{C}$

Doubt about finite normal extensions: proof of the going-down theorem

Semisimple endomorphism: Equivalent definitions?

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