Question

Degree of all extensions $\mathbb Q(\alpha)/\mathbb Q$ with $\alpha$ root of $T^5-T^4+3T^3+3T^2-9T+3$

score 44 · Answer 1 · 2026-04-17 06:13:38

44

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Degree of all extensions $\mathbb Q(\alpha)/\mathbb Q$ with $\alpha$ root of $T^5-T^4+3T^3+3T^2-9T+3$

Published on 17 Apr 2026 - 6:13

score 71 · Answer 2 · 2026-05-15 10:52:19

71

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Show a field extension is normal, then find the Galois group

Published on 15 May 2026 - 10:52

score 87 · Answer 3 · 2026-03-26 02:55:51

87

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Elements of a local field with trace in $\mathbb Z_p$

Published on 26 Mar 2026 - 2:55

score 68 · Answer 4 · 2026-04-28 10:55:39

68

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Help finding specific isomorphism between $\mathbb{Q}^{2g}$ and $K^2$.

Published on 28 Apr 2026 - 10:55

score 69 · Answer 5 · 2026-04-14 03:56:29

69

Views

Uniqueness of the Split Closure of a Field Extension

Published on 14 Apr 2026 - 3:56

score 72 · Answer 6 · 2026-03-27 01:00:17

72

Views

Let $E/L$ be an elliptic curve. Why is Galois cohomology $H^1(G,E(L))$ finite group?

Published on 27 Mar 2026 - 1:00

score 22 · Answer 7 · 2026-03-26 02:57:39

22

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Finding $\dfrac{\sigma(u)}{u}=\alpha$ for local field $K$, $L$ unramified over $K$, $\sigma$ being Frobenius of $L/K$ and $\alpha$ having norm 1.

Published on 26 Mar 2026 - 2:57

score 58 · Answer 8 · 2026-04-15 20:10:08

58

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Find a degree 3 polynomial that has a galois group of the extension field which is isomorfic to the ciclic group of order 3.

Published on 15 Apr 2026 - 20:10

score 331 · Answer 9 · 2026-04-13 20:46:32

331

Views

Does the Galois group of a quintic with a single real root contain $\mathbb{A}_5$?

Published on 13 Apr 2026 - 20:46

score 307 · Answer 10 · 2026-04-15 09:51:58

307

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How to find a $\mathbb{Q}$-basis for the splitting field of $x^4-2$ over $\mathbb{Q}$?

Published on 15 Apr 2026 - 9:51

score 72 · Answer 11 · 2026-04-15 12:36:24

72

Views

Degree of $F(x+y)$ over $F=k(x^3,y^3)$ in characteristic $2$

Published on 15 Apr 2026 - 12:36

score 159 · Answer 12 · 2026-04-16 16:13:25

159

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Does the Galois group act transitively on extensions of absolute values?

Published on 16 Apr 2026 - 16:13

score 57 · Answer 13 · 2026-04-13 07:07:01

57

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Basis of field extension

Published on 13 Apr 2026 - 7:07

score 45 · Answer 14 · 2026-04-16 02:22:31

45

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$p$ is irreducible and $p\mid bc$ follow that $p\mid b$ or $p\mid c$

Published on 16 Apr 2026 - 2:22

score 102 · Answer 15 · 2026-04-17 11:10:40

102

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Finite field extensions of degree 2

Published on 17 Apr 2026 - 11:10

List Question

Degree of all extensions $\mathbb Q(\alpha)/\mathbb Q$ with $\alpha$ root of $T^5-T^4+3T^3+3T^2-9T+3$

Show a field extension is normal, then find the Galois group

Elements of a local field with trace in $\mathbb Z_p$

Help finding specific isomorphism between $\mathbb{Q}^{2g}$ and $K^2$.

Uniqueness of the Split Closure of a Field Extension

Let $E/L$ be an elliptic curve. Why is Galois cohomology $H^1(G,E(L))$ finite group?

Finding $\dfrac{\sigma(u)}{u}=\alpha$ for local field $K$, $L$ unramified over $K$, $\sigma$ being Frobenius of $L/K$ and $\alpha$ having norm 1.

Find a degree 3 polynomial that has a galois group of the extension field which is isomorfic to the ciclic group of order 3.

Does the Galois group of a quintic with a single real root contain $\mathbb{A}_5$?

How to find a $\mathbb{Q}$-basis for the splitting field of $x^4-2$ over $\mathbb{Q}$?

Degree of $F(x+y)$ over $F=k(x^3,y^3)$ in characteristic $2$

Does the Galois group act transitively on extensions of absolute values?

Basis of field extension

$p$ is irreducible and $p\mid bc$ follow that $p\mid b$ or $p\mid c$

Finite field extensions of degree 2

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