Question

Proving that polynomial is irreducible over F and classifying its roots in a splitting field

score 451 · Answer 1 · 2016-05-19 22:23:28

451

Views

Proving that polynomial is irreducible over F and classifying its roots in a splitting field

Published on 19 May 2016 - 22:23

score 57 · Answer 2 · 2016-05-21 17:10:54

57

Views

For each polynomial $p \in K[t]$, there exists another polynomial $g$ such that $\{p(\epsilon_i): 1\leq i \leq n\}$ is its set of roots

Published on 21 May 2016 - 17:10

score 60 · Answer 3 · 2016-05-25 09:47:13

60

Views

Galois Group is $\mathbb{Z}/4\mathbb{Z}$.

Published on 25 May 2016 - 9:47

score 149 · Answer 4 · 2016-05-25 22:59:42

149

Views

Splitting field and automorphisms

Published on 25 May 2016 - 22:59

score 252 · Answer 5 · 2016-05-29 18:42:48

252

Views

Use Galois Theory to prove the existence of $A$ and $B$ such that $\mathbb{Q}(\sqrt{6+3\sqrt{3}})=\mathbb{Q}(\sqrt{A}, \sqrt{B})$

Published on 29 May 2016 - 18:42

score 30 · Answer 6 · 2016-05-30 09:35:57

30

Views

Prove that $L_f \vert E$ has degree $2$, or there are exactly three fields satisfying those conditions

Published on 30 May 2016 - 9:35

score 244 · Answer 7 · 2016-05-30 21:16:09

244

Views

$\mathbb{F_2}(\alpha)/\mathbb{F_2}$ is a splitting field of $f(x)$ over $\mathbb{F_2}$

Published on 30 May 2016 - 21:16

score 154 · Answer 8 · 2016-05-31 20:06:13

154

Views

Prove that $K$ is normal over $\mathbb{Q}$ and $K(i)=\mathbb{Q}(i, \sqrt[4]{A})$

Published on 31 May 2016 - 20:06

score 195 · Answer 9 · 2016-06-01 12:05:55

195

Views

Is there an algorithm to find the splitting field of a polynomial over galois finite fields?

Published on 01 Jun 2016 - 12:05

score 5.1k · Answer 10 · 2016-06-02 18:41:31

5.1k

Views

Galois groups of $x^3-3x+1$ and $(x^3-2)(x^2+3)$ over $\mathbb{Q}$

Published on 02 Jun 2016 - 18:41

score 420 · Answer 11 · 2016-06-02 20:17:41

420

Views

Minimal field extension of $\mathbb{Q}(\sqrt[6]{2})$ over $\mathbb{Q}$ and Galois group

Published on 02 Jun 2016 - 20:17

score 399 · Answer 12 · 2016-06-04 23:51:10

399

Views

Separable Extension and Splitting Field

Published on 04 Jun 2016 - 23:51

score 457 · Answer 13 · 2016-06-05 08:08:14

457

Views

Degree of Splitting Field of $x^{10}-5$ over $\mathbb{Q}$

Published on 05 Jun 2016 - 8:08

score 397 · Answer 14 · 2016-06-07 19:21:30

397

Views

Is $\sqrt{7} \in \mathbb{Q}\left(\sqrt{3+\sqrt{2}}\right)\;$?

Published on 07 Jun 2016 - 19:21

score 177 · Answer 15 · 2016-06-20 06:44:39

177

Views

Find a splitting field of $x^2 + 1$ over $\mathbb{Z}_3$

Published on 20 Jun 2016 - 6:44

List Question

Proving that polynomial is irreducible over F and classifying its roots in a splitting field

For each polynomial $p \in K[t]$, there exists another polynomial $g$ such that $\{p(\epsilon_i): 1\leq i \leq n\}$ is its set of roots

Galois Group is $\mathbb{Z}/4\mathbb{Z}$.

Splitting field and automorphisms

Use Galois Theory to prove the existence of $A$ and $B$ such that $\mathbb{Q}(\sqrt{6+3\sqrt{3}})=\mathbb{Q}(\sqrt{A}, \sqrt{B})$

Prove that $L_f \vert E$ has degree $2$, or there are exactly three fields satisfying those conditions

$\mathbb{F_2}(\alpha)/\mathbb{F_2}$ is a splitting field of $f(x)$ over $\mathbb{F_2}$

Prove that $K$ is normal over $\mathbb{Q}$ and $K(i)=\mathbb{Q}(i, \sqrt[4]{A})$

Is there an algorithm to find the splitting field of a polynomial over galois finite fields?

Galois groups of $x^3-3x+1$ and $(x^3-2)(x^2+3)$ over $\mathbb{Q}$

Minimal field extension of $\mathbb{Q}(\sqrt[6]{2})$ over $\mathbb{Q}$ and Galois group

Separable Extension and Splitting Field

Degree of Splitting Field of $x^{10}-5$ over $\mathbb{Q}$

Is $\sqrt{7} \in \mathbb{Q}\left(\sqrt{3+\sqrt{2}}\right)\;$?

Find a splitting field of $x^2 + 1$ over $\mathbb{Z}_3$

Trending Questions

Popular # Hahtags

Popular Questions