List questions from extension-field

Published on 11 Apr 2026 - 21:17

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Determine the degree of the splitting field for $f(x)=x^{15}-1$.

Published on 14 Apr 2026 - 10:01

892

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Is it true that $p\mid [\mathbb Q(\cos{\frac{\pi}{p^2}}):\mathbb Q]$?

Published on 14 Apr 2026 - 6:38

472

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Ramification in the ring of all algebraic integers

Published on 15 Apr 2026 - 4:59

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Let $F= \Bbb{Q}(\zeta_9)$ with $\zeta_9 = e^{\frac{2i\pi}{9}}$. Find the Galois group and the intermediate fields.

Published on 15 Apr 2026 - 8:48

435

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Algebraic Field Extensions

Published on 13 Apr 2026 - 12:53

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Determining A Splitting Field

Published on 08 Apr 2026 - 22:02

191

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Is $[\mathbb{R}:\mathbb{Q}]$ countable?

Published on 14 Apr 2026 - 4:42

822

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The simple extension $\mathbb Q(i+\sqrt{2})$

Published on 15 Apr 2026 - 19:00

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On the unicity of splitting field

Published on 13 Apr 2026 - 21:12

72

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perfect extensions of $\mathbb{F}_p$

Published on 16 Apr 2026 - 0:20

1.1k

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Regarding the normal closure of a finite extension

Published on 13 Apr 2026 - 5:25

683

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Is the real root of $x^4+3 x-3$ constructible?

Published on 13 Apr 2026 - 18:21

402

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Compositum of normal extensions and embedding

Published on 09 Apr 2026 - 21:53

192

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$[E:\mathbb{Q}]$, the degree of $E$ over $\mathbb{Q}$

Published on 16 Apr 2026 - 9:36

List Question

Understanding Dummit & Foote p.528 Sec 13.2 Algebraic Extensions

Determine the degree of the splitting field for $f(x)=x^{15}-1$.

Is it true that $p\mid [\mathbb Q(\cos{\frac{\pi}{p^2}}):\mathbb Q]$?

Ramification in the ring of all algebraic integers

Let $F= \Bbb{Q}(\zeta_9)$ with $\zeta_9 = e^{\frac{2i\pi}{9}}$. Find the Galois group and the intermediate fields.

Algebraic Field Extensions

Determining A Splitting Field

Is $[\mathbb{R}:\mathbb{Q}]$ countable?

The simple extension $\mathbb Q(i+\sqrt{2})$

On the unicity of splitting field

perfect extensions of $\mathbb{F}_p$

Regarding the normal closure of a finite extension

Is the real root of $x^4+3 x-3$ constructible?

Compositum of normal extensions and embedding

$[E:\mathbb{Q}]$, the degree of $E$ over $\mathbb{Q}$

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