List questions from extension-field

Published on 13 Mar 2018 - 13:33

43

Views

$E=F(\alpha_1, \cdots, \alpha_n)$ where $\alpha_1, \cdots, \alpha_n$ are distinct and separable over $F$

Published on 14 Mar 2018 - 5:09

44

Views

A property regarding $\mathbb{Q}(\sqrt{x})$

Published on 14 Mar 2018 - 5:49

353

Views

Basis over GF(2^5) with sum of its elements = 1

Published on 25 Mar 2026 - 3:19

293

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Irreducible polynomial over $GF(32)$

Published on 25 Mar 2026 - 3:19

442

Views

Is this the (real) algebraic numbers?

Published on 17 Mar 2018 - 16:09

168

Views

Axiomatize purely transcendental field extension

Published on 17 Mar 2018 - 17:55

36

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$f(x)=x^{p^n}-b$ is irreducible

Published on 25 Mar 2026 - 3:22

669

Views

Finitely generated extension of transcendence degree 1

Published on 18 Mar 2018 - 22:58

64

Views

Field generated and fraction field

Published on 19 Mar 2018 - 5:13

439

Views

Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?

Published on 25 Mar 2026 - 3:20

261

Views

How to prove that $\sqrt{p_n} \notin \mathbb{Q}(\sqrt{p_1},\dots,\sqrt{p_{n-1}})$

Published on 21 Mar 2018 - 6:57

460

Views

splitting field of $(x^2-3)(x^2-5)$ over $Q(\sqrt{ 2})$. Am I thinking of this correctly?

Published on 22 Mar 2018 - 17:00

230

Views

Is $i\sqrt[4]{10} \in \Bbb Q(\sqrt[4]{10})$ or is my proof wrong?

Published on 22 Mar 2018 - 20:25

106

Views

How much do you need to prove when finding splitting fields?

Published on 22 Mar 2018 - 21:57

List Question

Find the minimal polynomial for the roots $\sqrt{2}$ and $\sqrt{3}$ over $\mathbb{Q}$.

$E=F(\alpha_1, \cdots, \alpha_n)$ where $\alpha_1, \cdots, \alpha_n$ are distinct and separable over $F$

A property regarding $\mathbb{Q}(\sqrt{x})$

Basis over GF(2^5) with sum of its elements = 1

Irreducible polynomial over $GF(32)$

Is this the (real) algebraic numbers?

Axiomatize purely transcendental field extension

$f(x)=x^{p^n}-b$ is irreducible

Finitely generated extension of transcendence degree 1

Field generated and fraction field

Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?

How to prove that $\sqrt{p_n} \notin \mathbb{Q}(\sqrt{p_1},\dots,\sqrt{p_{n-1}})$

splitting field of $(x^2-3)(x^2-5)$ over $Q(\sqrt{ 2})$. Am I thinking of this correctly?

Is $i\sqrt[4]{10} \in \Bbb Q(\sqrt[4]{10})$ or is my proof wrong?

How much do you need to prove when finding splitting fields?

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