Question

$\mathbb{Q}(\alpha)\cap\mathbb{R}=\mathbb{Q}$, where $\alpha=\sqrt{\frac{3+\sqrt{7}i}{2}}$

score 87 · Answer 1 · 2026-03-31 15:23:35

87

Views

$\mathbb{Q}(\alpha)\cap\mathbb{R}=\mathbb{Q}$, where $\alpha=\sqrt{\frac{3+\sqrt{7}i}{2}}$

Published on 31 Mar 2026 - 15:23

score 144 · Answer 2 · 2026-03-31 15:24:55

144

Views

Show that there exists an $\alpha \in K$ such that $\alpha^2 \in F$ but $\alpha \notin F$

Published on 31 Mar 2026 - 15:24

score 572 · Answer 3 · 2019-04-17 01:08:01

572

Views

Computing $\phi(\frac32)$ where $\phi$ is an automorphism of $\mathbb Q[\sqrt2]$ such that $\phi(1)=1$ and $\phi(\sqrt2)=\sqrt2$

Published on 17 Apr 2019 - 1:08

score 731 · Answer 4 · 2026-03-28 01:02:53

731

Views

Show that $E/F$ is Galois extension

Published on 28 Mar 2026 - 1:02

score 78 · Answer 5 · 2026-03-25 22:25:10

78

Views

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

Published on 25 Mar 2026 - 22:25

score 455 · Answer 6 · 2026-03-28 01:02:52

455

Views

A question regarding the Galois extension of the cyclotomic polynomial $\Phi_{15}$

Published on 28 Mar 2026 - 1:02

score 58 · Answer 7 · 2026-03-25 23:36:07

58

Views

Galois cover and solvability

Published on 25 Mar 2026 - 23:36

score 116 · Answer 8 · 2026-03-28 01:02:53

116

Views

Condition on Galois Group that makes polynomial irreducible

Published on 28 Mar 2026 - 1:02

score 242 · Answer 9 · 2026-03-25 06:04:41

242

Views

What is the Galois group of the Hyperreal Numbers?

Published on 25 Mar 2026 - 6:04

score 135 · Answer 10 · 2019-04-19 04:53:51

135

Views

Prove that the composition of Galois extensions is not neccessarily Galois

Published on 19 Apr 2019 - 4:53

score 64 · Answer 11 · 2026-03-25 23:58:39

64

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 25 Mar 2026 - 23:58

score 228 · Answer 12 · 2026-03-25 14:21:50

228

Views

Completing Algebraic Integers into Squares

Published on 25 Mar 2026 - 14:21

score 314 · Answer 13 · 2026-03-25 13:34:20

314

Views

Why are the Galois groups that correspond to extensions which adjoin primitive roots of unity given by the group of units mod n

Published on 25 Mar 2026 - 13:34

score 160 · Answer 14 · 2019-04-19 21:37:37

160

Views

Galois Theory for Finite Extensions of Rings

Published on 19 Apr 2019 - 21:37

score 499 · Answer 15 · 2026-03-25 22:26:08

499

Views

When degree of splitting field equals n factorial

Published on 25 Mar 2026 - 22:26

List Question

$\mathbb{Q}(\alpha)\cap\mathbb{R}=\mathbb{Q}$, where $\alpha=\sqrt{\frac{3+\sqrt{7}i}{2}}$

Show that there exists an $\alpha \in K$ such that $\alpha^2 \in F$ but $\alpha \notin F$

Computing $\phi(\frac32)$ where $\phi$ is an automorphism of $\mathbb Q[\sqrt2]$ such that $\phi(1)=1$ and $\phi(\sqrt2)=\sqrt2$

Show that $E/F$ is Galois extension

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

A question regarding the Galois extension of the cyclotomic polynomial $\Phi_{15}$

Galois cover and solvability

Condition on Galois Group that makes polynomial irreducible

What is the Galois group of the Hyperreal Numbers?

Prove that the composition of Galois extensions is not neccessarily Galois

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 $F\cong K$?

Completing Algebraic Integers into Squares

Why are the Galois groups that correspond to extensions which adjoin primitive roots of unity given by the group of units mod n

Galois Theory for Finite Extensions of Rings

When degree of splitting field equals n factorial

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