Question

Question about determining $[\Bbb Q(\sqrt[3]2, \sqrt[4]3) : \Bbb Q]$

score 134 · Answer 1 · 2026-04-16 10:08:09

134

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Question about determining $[\Bbb Q(\sqrt[3]2, \sqrt[4]3) : \Bbb Q]$

Published on 16 Apr 2026 - 10:08

score 184 · Answer 2 · 2026-04-13 17:54:03

184

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Determine the Galois group of $F$ over $E$

Published on 13 Apr 2026 - 17:54

score 50 · Answer 3 · 2026-04-12 18:09:17

50

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When does the symmetrisation generate an intermediate field?

Published on 12 Apr 2026 - 18:09

score 792 · Answer 4 · 2026-04-13 22:44:25

792

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Separable closure and normality

Published on 13 Apr 2026 - 22:44

score 171 · Answer 5 · 2026-04-12 22:35:49

171

Views

Proving $\sqrt{6}$ is not part of a field

Published on 12 Apr 2026 - 22:35

score 90 · Answer 6 · 2026-04-14 22:18:32

90

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What is the smallest element of $\{n\in \mathbb N^*\mid \underbrace{1+...+1}_{n\ times}=0\}$

Published on 14 Apr 2026 - 22:18

score 56 · Answer 7 · 2026-04-08 23:09:16

56

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Understanding the definition of a field

Published on 08 Apr 2026 - 23:09

score 637 · Answer 8 · 2026-04-17 13:52:15

637

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Find a field with $a,b$ in an extension field such that $F(a, b) \neq F(a), F(a, b) \neq F(b)$, and $[F(a, b):F] \lt [F(a):F][F(b):F]$

Published on 17 Apr 2026 - 13:52

score 280 · Answer 9 · 2026-04-11 06:32:13

280

Views

Are there irreducible polynomials of "infinite" degree?

Published on 11 Apr 2026 - 6:32

score 161 · Answer 10 · 2026-04-08 01:16:06

161

Views

Understanding the statement of a corollary from Dummit and Foote's Abstract Algebra third edition

Published on 08 Apr 2026 - 1:16

score 223 · Answer 11 · 2026-04-16 21:36:00

223

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If $[E_1:F]$ and $[E_2:F]$ are both prime, show that $E_1 = E_2$ or $E_1 \cap E_2 = F$

Published on 16 Apr 2026 - 21:36

score 2.3k · Answer 12 · 2026-04-14 11:08:38

2.3k

Views

Is there a special name for a field where each number has a square root?

Published on 14 Apr 2026 - 11:08

score 838 · Answer 13 · 2026-04-12 10:46:36

838

Views

Is the square root of a complex number over a field always well-defined?

Published on 12 Apr 2026 - 10:46

score 79 · Answer 14 · 2026-04-14 16:16:20

79

Views

Irreducible Plane Curves Over the Algebraic $p$-adic Numbers

Published on 14 Apr 2026 - 16:16

score 568 · Answer 15 · 2026-04-17 03:17:39

568

Views

If $[E:F] = n$ and $p(x)$ is irreducible over $F$ and $\gcd(n, \deg p(x)) = 1$, then $[E(a) : E] \le [F(a) : F] = \deg f(x)$

Published on 17 Apr 2026 - 3:17

List Question

Question about determining $[\Bbb Q(\sqrt[3]2, \sqrt[4]3) : \Bbb Q]$

Determine the Galois group of $F$ over $E$

When does the symmetrisation generate an intermediate field?

Separable closure and normality

Proving $\sqrt{6}$ is not part of a field

What is the smallest element of $\{n\in \mathbb N^*\mid \underbrace{1+...+1}_{n\ times}=0\}$

Understanding the definition of a field

Find a field with $a,b$ in an extension field such that $F(a, b) \neq F(a), F(a, b) \neq F(b)$, and $[F(a, b):F] \lt [F(a):F][F(b):F]$

Are there irreducible polynomials of "infinite" degree?

Understanding the statement of a corollary from Dummit and Foote's Abstract Algebra third edition

If $[E_1:F]$ and $[E_2:F]$ are both prime, show that $E_1 = E_2$ or $E_1 \cap E_2 = F$

Is there a special name for a field where each number has a square root?

Is the square root of a complex number over a field always well-defined?

Irreducible Plane Curves Over the Algebraic $p$-adic Numbers

If $[E:F] = n$ and $p(x)$ is irreducible over $F$ and $\gcd(n, \deg p(x)) = 1$, then $[E(a) : E] \le [F(a) : F] = \deg f(x)$

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