Question

If $[K:F]=p^{2}q$, where $p$ and $q$ are distinct primes, show that $K$ has subfields $L_{1}, L_{2}$ and $L_{3}$

score 155 · Answer 1 · 2021-11-24 15:22:50

155

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If $[K:F]=p^{2}q$, where $p$ and $q$ are distinct primes, show that $K$ has subfields $L_{1}, L_{2}$ and $L_{3}$

Published on 24 Nov 2021 - 15:22

score 343 · Answer 2 · 2021-11-25 04:06:18

343

Views

Galois group of splitting field of $X^4 -6X^2 -2$

Published on 25 Nov 2021 - 4:06

score 287 · Answer 3 · 2021-11-29 10:44:31

287

Views

Determine the splitting field and its degree over $\mathbb Q$ for $x^6 - 4.$

Published on 29 Nov 2021 - 10:44

score 119 · Answer 4 · 2026-04-01 15:08:56

119

Views

Automorphism of a splitting field of a polynomial

Published on 01 Apr 2026 - 15:08

score 66 · Answer 5 · 2021-12-05 14:34:00

66

Views

Rupture field of an irreducible polynomial over a finite field equals its splitting field

Published on 05 Dec 2021 - 14:34

score 69 · Answer 6 · 2021-12-13 20:22:40

69

Views

Question on why a field extension isn't a splitting field (and on general behavior of field extensions)

Published on 13 Dec 2021 - 20:22

score 66 · Answer 7 · 2021-12-31 22:06:50

66

Views

How many degree $k$, monic polynomials factor completely in $\mathbb{Z}/p\mathbb{Z}$?

Published on 31 Dec 2021 - 22:06

score 84 · Answer 8 · 2022-01-05 01:43:50

84

Views

Splitting Field of $x^6 + x^3 + 2$ over $\mathbb{F}_3$

Published on 05 Jan 2022 - 1:43

score 223 · Answer 9 · 2022-01-05 02:52:42

223

Views

If the Galois group is $S_3$, can the extension be realized as the splitting field of a cubic?

Published on 05 Jan 2022 - 2:52

score 288 · Answer 10 · 2022-01-05 17:41:52

288

Views

Find the splitting field of $x^4-4x^2+1$ over $\mathbb{Q}$

Published on 05 Jan 2022 - 17:41

score 86 · Answer 11 · 2022-01-08 16:23:23

86

Views

Order of field extension

Published on 08 Jan 2022 - 16:23

score 58 · Answer 12 · 2022-01-09 21:21:48

58

Views

Let $\sigma\in{\rm Gal}(E/\Bbb Q)$ s.t. $\sigma(\alpha)=\bar\alpha$ for all $\alpha\in E$. Find ${\rm Inv}(\langle\sigma\rangle)$

Published on 09 Jan 2022 - 21:21

score 189 · Answer 13 · 2022-01-14 16:50:28

189

Views

How should I have known that $x^4-2x^3-7x^2+10x+10=(x^2-2x-2)(x^2-5)$?

Published on 14 Jan 2022 - 16:50

score 727 · Answer 14 · 2022-01-16 02:39:02

727

Views

Find the splitting field $E$ of $x^6-4$ over $\mathbb{Q}$ and determine the dimension of $E$ over $\mathbb{Q}.$

Published on 16 Jan 2022 - 2:39

score 93 · Answer 15 · 2022-01-26 14:30:31

93

Views

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

Published on 26 Jan 2022 - 14:30

List Question

If $[K:F]=p^{2}q$, where $p$ and $q$ are distinct primes, show that $K$ has subfields $L_{1}, L_{2}$ and $L_{3}$

Galois group of splitting field of $X^4 -6X^2 -2$

Determine the splitting field and its degree over $\mathbb Q$ for $x^6 - 4.$

Automorphism of a splitting field of a polynomial

Rupture field of an irreducible polynomial over a finite field equals its splitting field

Question on why a field extension isn't a splitting field (and on general behavior of field extensions)

How many degree $k$, monic polynomials factor completely in $\mathbb{Z}/p\mathbb{Z}$?

Splitting Field of $x^6 + x^3 + 2$ over $\mathbb{F}_3$

If the Galois group is $S_3$, can the extension be realized as the splitting field of a cubic?

Find the splitting field of $x^4-4x^2+1$ over $\mathbb{Q}$

Order of field extension

Let $\sigma\in{\rm Gal}(E/\Bbb Q)$ s.t. $\sigma(\alpha)=\bar\alpha$ for all $\alpha\in E$. Find ${\rm Inv}(\langle\sigma\rangle)$

How should I have known that $x^4-2x^3-7x^2+10x+10=(x^2-2x-2)(x^2-5)$?

Find the splitting field $E$ of $x^6-4$ over $\mathbb{Q}$ and determine the dimension of $E$ over $\mathbb{Q}.$

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

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