Question

How to find the splitting field for $x^3-x^2-x-2$ over $\Bbb Q$?

score 40 · Answer 1 · 2026-04-16 03:16:39

40

Views

How to find the splitting field for $x^3-x^2-x-2$ over $\Bbb Q$?

Published on 16 Apr 2026 - 3:16

score 111 · Answer 2 · 2026-05-11 04:07:04

111

Views

Finding all polynomials $p(x)$ such that $ \mathbb{Q}[x]/p(x) \simeq \mathbb{Q}(A)$ for fixed $A$ algebraic

Published on 11 May 2026 - 4:07

score 1k · Answer 3 · 2026-04-09 19:48:18

1k

Views

Splitting field/subfield is isomorphic

Published on 09 Apr 2026 - 19:48

score 35 · Answer 4 · 2026-04-13 04:28:18

35

Views

Relationship between $\Bbb Q(\sqrt2)$ and the splitting field of $x^2-2$

Published on 13 Apr 2026 - 4:28

score 198 · Answer 5 · 2026-04-14 02:43:38

198

Views

Galois / Splitting field of $\ \sqrt{\vphantom{\sum}2+{\sqrt2}} $

Published on 14 Apr 2026 - 2:43

score 210 · Answer 6 · 2026-04-16 04:09:20

210

Views

Show that $E/F$ is an abelian Galois extension such that $G=\text{Gal}(E/F)$ has exponent $m$ dividing $n$

Published on 16 Apr 2026 - 4:09

score 314 · Answer 7 · 2026-04-16 06:44:13

314

Views

Efficiently calculating the Galois group of $p(x)=x^4+4x^2-2$

Published on 16 Apr 2026 - 6:44

score 692 · Answer 8 · 2026-05-10 19:51:41

692

Views

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

Published on 10 May 2026 - 19:51

score 412 · Answer 9 · 2026-04-16 07:24:50

412

Views

If $f \in F[x]$ irreducible, ${\rm char}(F) = p$, then $f(x) = g(x^{p^e})$ and every root of $f$ has multiplicity $p^e$ in some splitting field

Published on 16 Apr 2026 - 7:24

score 654 · Answer 10 · 2026-04-16 21:19:25

654

Views

Splitting field of $\sqrt{\vphantom{\sum}1+{\sqrt2}}$ and Galois group

Published on 16 Apr 2026 - 21:19

score 310 · Answer 11 · 2026-04-17 02:45:35

310

Views

Prove that $[\mathbf{Q}(\sqrt{1+i},\sqrt{2}):\mathbf{Q}]=8$.

Published on 17 Apr 2026 - 2:45

score 127 · Answer 12 · 2026-04-14 18:18:37

127

Views

Tower of Splitting Fields

Published on 14 Apr 2026 - 18:18

score 80 · Answer 13 · 2026-04-12 10:57:09

80

Views

Clarification on normality and separability in the context of field extensions.

Published on 12 Apr 2026 - 10:57

score 66 · Answer 14 · 2026-04-15 06:36:18

66

Views

For a field $K$ of characteristics $p>0$, when is a finite purely inseparable extension $F/K$ (with $[F:K]=p^n>1$) such that $F\cong K$?

Published on 15 Apr 2026 - 6:36

score 503 · Answer 15 · 2026-04-17 07:10:00

503

Views

When degree of splitting field equals n factorial

Published on 17 Apr 2026 - 7:10

List Question

How to find the splitting field for $x^3-x^2-x-2$ over $\Bbb Q$?

Finding all polynomials $p(x)$ such that $ \mathbb{Q}[x]/p(x) \simeq \mathbb{Q}(A)$ for fixed $A$ algebraic

Splitting field/subfield is isomorphic

Relationship between $\Bbb Q(\sqrt2)$ and the splitting field of $x^2-2$

Galois / Splitting field of $\ \sqrt{\vphantom{\sum}2+{\sqrt2}} $

Show that $E/F$ is an abelian Galois extension such that $G=\text{Gal}(E/F)$ has exponent $m$ dividing $n$

Efficiently calculating the Galois group of $p(x)=x^4+4x^2-2$

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

If $f \in F[x]$ irreducible, ${\rm char}(F) = p$, then $f(x) = g(x^{p^e})$ and every root of $f$ has multiplicity $p^e$ in some splitting field

Splitting field of $\sqrt{\vphantom{\sum}1+{\sqrt2}}$ and Galois group

Prove that $[\mathbf{Q}(\sqrt{1+i},\sqrt{2}):\mathbf{Q}]=8$.

Tower of Splitting Fields

Clarification on normality and separability in the context of field extensions.

For a field $K$ of characteristics $p>0$, when is a finite purely inseparable extension $F/K$ (with $[F:K]=p^n>1$) such that $F\cong K$?

When degree of splitting field equals n factorial

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