Question

Compute the degree of the extension $\mathbb{Q}\left(\sqrt{1+i\sqrt3}+\sqrt{1-i\sqrt3}\right)$ over $\mathbb{Q}$

score 50 · Answer 1 · 2026-04-15 15:05:02

50

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Compute the degree of the extension $\mathbb{Q}\left(\sqrt{1+i\sqrt3}+\sqrt{1-i\sqrt3}\right)$ over $\mathbb{Q}$

Published on 15 Apr 2026 - 15:05

score 93 · Answer 2 · 2026-04-24 01:10:29

93

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Example of $f \in K[x]$ solvable by radicals but having a root that cannot be expressed by using only coefficients of $f$, $+,-,\cdot,\frac{..}{..}$

Published on 24 Apr 2026 - 1:10

score 288 · Answer 3 · 2026-04-24 01:11:35

288

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Example of $f \in K[x]$ solvable by radicals but having a root inexpressible only by coefficients of $f$ and +, -, *, /, $\sqrt[n]{...}$

Published on 24 Apr 2026 - 1:11

score 132 · Answer 4 · 2026-04-15 04:20:24

132

Views

If $L/K$ is a field extension then $\operatorname{char}(L) = \operatorname{char}(K)$

Published on 15 Apr 2026 - 4:20

score 158 · Answer 5 · 2026-04-14 02:56:39

158

Views

Minimal polynomial of $x$ over $K(f(x))$

Published on 14 Apr 2026 - 2:56

score 32 · Answer 6 · 2026-04-16 11:22:21

32

Views

Why is $\left[\mathbb{R}(t):\mathbb{R} \right]$ infinite?

Published on 16 Apr 2026 - 11:22

score 474 · Answer 7 · 2026-04-10 14:11:20

474

Views

Krull Topology on a Galois Group Definition

Published on 10 Apr 2026 - 14:11

score 45 · Answer 8 · 2026-04-15 00:38:32

45

Views

smallest subfield contains open interval

Published on 15 Apr 2026 - 0:38

score 202 · Answer 9 · 2026-04-24 01:02:57

202

Views

Rationalizing General Denominators

Published on 24 Apr 2026 - 1:02

score 58 · Answer 10 · 2026-04-16 10:38:14

58

Views

Fastest way to find the order of x in a Finite Field

Published on 16 Apr 2026 - 10:38

score 42 · Answer 11 · 2026-04-12 20:49:00

42

Views

suppose K is an extension field of finite degree, and L,H are middle fields such that L(H)＝K.Prove that [K:L]≤[H:F]

Published on 12 Apr 2026 - 20:49

score 106 · Answer 12 · 2026-04-15 18:11:07

106

Views

Prove that $x^{p^{n}}-x-a$ is reducible over GF(p).

Published on 15 Apr 2026 - 18:11

score 95 · Answer 13 · 2026-04-12 09:46:25

95

Views

Understanding some square root notation in LMFDB occuring in the definition of a p-adic field

Published on 12 Apr 2026 - 9:46

score 93 · Answer 14 · 2026-04-17 22:20:24

93

Views

Prove via ultraproducts that the class of algebraic extensions is not axiomatisable in the language of rings

Published on 17 Apr 2026 - 22:20

score 198 · Answer 15 · 2026-04-15 18:29:40

198

Views

$\mathbb{Q}(\pi) \subsetneq \mathbb{Q}(\sqrt {\pi})$?

Published on 15 Apr 2026 - 18:29

List Question

Compute the degree of the extension $\mathbb{Q}\left(\sqrt{1+i\sqrt3}+\sqrt{1-i\sqrt3}\right)$ over $\mathbb{Q}$

Example of $f \in K[x]$ solvable by radicals but having a root that cannot be expressed by using only coefficients of $f$, $+,-,\cdot,\frac{..}{..}$

Example of $f \in K[x]$ solvable by radicals but having a root inexpressible only by coefficients of $f$ and +, -, *, /, $\sqrt[n]{...}$

If $L/K$ is a field extension then $\operatorname{char}(L) = \operatorname{char}(K)$

Minimal polynomial of $x$ over $K(f(x))$

Why is $\left[\mathbb{R}(t):\mathbb{R} \right]$ infinite?

Krull Topology on a Galois Group Definition

smallest subfield contains open interval

Rationalizing General Denominators

Fastest way to find the order of x in a Finite Field

suppose K is an extension field of finite degree, and L,H are middle fields such that L(H)＝K.Prove that [K:L]≤[H:F]

Prove that $x^{p^{n}}-x-a$ is reducible over GF(p).

Understanding some square root notation in LMFDB occuring in the definition of a p-adic field

Prove via ultraproducts that the class of algebraic extensions is not axiomatisable in the language of rings

$\mathbb{Q}(\pi) \subsetneq \mathbb{Q}(\sqrt {\pi})$?

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