List questions from splitting-field

Published on 24 Apr 2014 - 0:42

2.6k

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Let $K = \mathbb{Q}(\alpha)$ where $\alpha$ is a root of the polynomial $x^3 + 2x + 1$, and let $g(x) = x^3 + x + 1$. Does $g(x)$ have a root in $K$?

Published on 26 Apr 2014 - 22:32

267

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Understanding a Solution (Splitting Fields)

Published on 28 Apr 2014 - 9:39

81

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can we have split field of the real number and how i get the extension dimension?

Published on 01 May 2014 - 1:17

596

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show the splitting field of polynomial

Published on 01 May 2014 - 2:09

297

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Find the splitting Field of $x^4+x^2+1$

Published on 01 May 2014 - 5:54

160

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Geometric meaning of the splitting field over a function field

Published on 24 Mar 2026 - 23:55

1.1k

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Splitting field of cyclotomic polynomials over $\mathbb{F}_2$.

Published on 22 May 2014 - 7:13

191

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When is a number in $\mathbb{Q}(\sqrt{a_1},\ldots,\sqrt{a_n})$?

Published on 22 May 2014 - 11:27

411

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Simple field extension and roots of a polynomial

Published on 01 Jun 2014 - 9:40

3.2k

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Find all subfields in extension $\mathbb{Q}\subseteq \mathbb{Q}(\sqrt[4]{2})$

Published on 01 Jun 2014 - 13:38

1.1k

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Splitting Field of Cubic Polynomial Over the Rationals

Published on 28 Jun 2014 - 16:11

1k

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Automorphisms of splitting field of $x^p-x-a$

Published on 09 Aug 2014 - 21:03

299

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Counting the roots of a polynomial over a finite field

Published on 20 Aug 2014 - 23:15

89

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Splitting field of $(x^2-2)(x^6-20)$ over $\mathbb{Q}$

Published on 24 Aug 2014 - 22:02

List Question

Degree of $\mathbb{Q}(\sqrt[3]{2}, \sqrt{-3})$ over $\mathbb{Q}(\sqrt[3]{2})$

Let $K = \mathbb{Q}(\alpha)$ where $\alpha$ is a root of the polynomial $x^3 + 2x + 1$, and let $g(x) = x^3 + x + 1$. Does $g(x)$ have a root in $K$?

Understanding a Solution (Splitting Fields)

can we have split field of the real number and how i get the extension dimension?

show the splitting field of polynomial

Find the splitting Field of $x^4+x^2+1$

Geometric meaning of the splitting field over a function field

Splitting field of cyclotomic polynomials over $\mathbb{F}_2$.

When is a number in $\mathbb{Q}(\sqrt{a_1},\ldots,\sqrt{a_n})$?

Simple field extension and roots of a polynomial

Find all subfields in extension $\mathbb{Q}\subseteq \mathbb{Q}(\sqrt[4]{2})$

Splitting Field of Cubic Polynomial Over the Rationals

Automorphisms of splitting field of $x^p-x-a$

Counting the roots of a polynomial over a finite field

Splitting field of $(x^2-2)(x^6-20)$ over $\mathbb{Q}$

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