Question

Suppose that both $a$ and $a^2$ are roots of an irreducible polynomial $f$ over $\mathbb{Q}$. Show that $a^4,a^8....$ are also roots of f

score 94 · Answer 1 · 2017-02-23 20:49:47

94

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Suppose that both $a$ and $a^2$ are roots of an irreducible polynomial $f$ over $\mathbb{Q}$. Show that $a^4,a^8....$ are also roots of f

Published on 23 Feb 2017 - 20:49

score 189 · Answer 2 · 2017-02-26 15:39:27

189

Views

Galois extenstion of rational function field $\mathbb{C}(X,Y,Z)$

Published on 26 Feb 2017 - 15:39

score 207 · Answer 3 · 2017-03-08 03:51:00

207

Views

Splitting field of polynomial generated by just one of its roots

Published on 08 Mar 2017 - 3:51

score 92 · Answer 4 · 2017-03-12 04:28:45

92

Views

One zero in extension field $F$ implies other zero in $F$

Published on 12 Mar 2017 - 4:28

score 55 · Answer 5 · 2017-03-13 15:11:43

55

Views

Understanding this theorem indicating the simplicity of a field extension

Published on 13 Mar 2017 - 15:11

score 494 · Answer 6 · 2017-03-14 20:56:36

494

Views

Zeroes of irreducible polynomial over splitting field

Published on 14 Mar 2017 - 20:56

score 182 · Answer 7 · 2026-02-23 01:05:17

182

Views

A finite extension of a normal extension is normal?

Published on 23 Feb 2026 - 1:05

score 418 · Answer 8 · 2017-03-22 11:21:06

418

Views

Is this proof on the insolvability of the quintic equation correct?

Published on 22 Mar 2017 - 11:21

score 190 · Answer 9 · 2017-03-24 08:47:38

190

Views

Degree of a splitting field over $ \mathbb{F}_{4}(t)$

Published on 24 Mar 2017 - 8:47

score 703 · Answer 10 · 2017-03-24 17:23:29

703

Views

Show that Galois Group $G(K/Q)$ of K over Q is isomorphic to symetric group $S_3$

Published on 24 Mar 2017 - 17:23

score 25 · Answer 11 · 2017-03-27 05:42:50

25

Views

Show degree of a field extension over the rationals

Published on 27 Mar 2017 - 5:42

score 277 · Answer 12 · 2017-03-27 15:35:05

277

Views

Degree of field extension over the rationals

Published on 27 Mar 2017 - 15:35

score 59 · Answer 13 · 2017-03-28 01:43:16

59

Views

Is $F(c)=F[c]$?

Published on 28 Mar 2017 - 1:43

score 418 · Answer 14 · 2017-03-28 07:12:05

418

Views

Find splitting field of a cubic polynomial

Published on 28 Mar 2017 - 7:12

score 675 · Answer 15 · 2017-03-30 04:29:29

675

Views

Finding one primitive element for splitting field of polynomial over $\mathbb{Q}$

Published on 30 Mar 2017 - 4:29

List Question

Suppose that both $a$ and $a^2$ are roots of an irreducible polynomial $f$ over $\mathbb{Q}$. Show that $a^4,a^8....$ are also roots of f

Galois extenstion of rational function field $\mathbb{C}(X,Y,Z)$

Splitting field of polynomial generated by just one of its roots

One zero in extension field $F$ implies other zero in $F$

Understanding this theorem indicating the simplicity of a field extension

Zeroes of irreducible polynomial over splitting field

A finite extension of a normal extension is normal?

Is this proof on the insolvability of the quintic equation correct?

Degree of a splitting field over $ \mathbb{F}_{4}(t)$

Show that Galois Group $G(K/Q)$ of K over Q is isomorphic to symetric group $S_3$

Show degree of a field extension over the rationals

Degree of field extension over the rationals

Is $F(c)=F[c]$?

Find splitting field of a cubic polynomial

Finding one primitive element for splitting field of polynomial over $\mathbb{Q}$

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