Question

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

score 37 · Answer 1 · 2019-03-24 21:41:18

37

Views

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

Published on 24 Mar 2019 - 21:41

score 108 · Answer 2 · 2019-03-24 23:40:08

108

Views

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

Published on 24 Mar 2019 - 23:40

score 1k · Answer 3 · 2019-03-28 00:36:38

1k

Views

Splitting field/subfield is isomorphic

Published on 28 Mar 2019 - 0:36

score 33 · Answer 4 · 2019-03-28 05:46:34

33

Views

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

Published on 28 Mar 2019 - 5:46

score 195 · Answer 5 · 2019-03-31 19:54:41

195

Views

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

Published on 31 Mar 2019 - 19:54

score 207 · Answer 6 · 2019-04-06 20:46:58

207

Views

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

Published on 06 Apr 2019 - 20:46

score 311 · Answer 7 · 2019-04-09 05:22:18

311

Views

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

Published on 09 Apr 2019 - 5:22

score 691 · Answer 8 · 2026-03-25 11:06:38

691

Views

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

Published on 25 Mar 2026 - 11:06

score 408 · Answer 9 · 2019-04-09 16:21:29

408

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 09 Apr 2019 - 16:21

score 649 · Answer 10 · 2019-04-15 01:16:42

649

Views

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

Published on 15 Apr 2019 - 1:16

score 307 · Answer 11 · 2019-04-15 16:58:22

307

Views

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

Published on 15 Apr 2019 - 16:58

score 124 · Answer 12 · 2019-04-17 12:01:17

124

Views

Tower of Splitting Fields

Published on 17 Apr 2019 - 12:01

score 77 · Answer 13 · 2019-04-17 19:57:17

77

Views

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

Published on 17 Apr 2019 - 19:57

score 62 · Answer 14 · 2019-04-19 15:27:08

62

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 19 Apr 2019 - 15:27

score 498 · Answer 15 · 2019-04-20 05:45:59

498

Views

When degree of splitting field equals n factorial

Published on 20 Apr 2019 - 5:45

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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