List questions from extension-field

Published on 30 Mar 2026 - 0:52

152

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Are coprime polynomials also coprime considered in the algebraic closure?

Published on 18 Dec 2019 - 16:07

621

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Questions about the proof of $a+b$ and $ab$ (transcendental/algebraic)

Published on 18 Dec 2019 - 16:50

30

Views

Minimal polynomial over $\mathbb{Q}$ (Computing)

Published on 30 Mar 2026 - 2:47

147

Views

$a+b$ and $ab$ are not both algebraic over $K$ (proof)

Published on 30 Mar 2026 - 0:57

514

Views

General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$

Published on 20 Dec 2019 - 2:35

283

Views

Maximal algebraic ordered field extensions of $\mathbb{Q}$

Published on 25 Mar 2026 - 16:45

66

Views

Proving equivalence between finite field extensions.

Published on 23 Feb 2026 - 6:36

143

Views

Finite field extension that is properly contained in a splitting field

Published on 26 Mar 2026 - 12:58

83

Views

Determine the splitting field (polynomial/degree)

Published on 22 Dec 2019 - 17:15

36

Views

Conditions for being an unramified extensions

Published on 23 Dec 2019 - 19:26

51

Views

A question on field and subfields

Published on 24 Dec 2019 - 16:59

134

Views

Simple question about Galois theory

Published on 26 Dec 2019 - 16:33

230

Views

Lang's definition of separability (solved)

Published on 23 Feb 2026 - 4:53

317

Views

Prove that $\sqrt{p_n}\not\in \mathbb{Q}(\sqrt{p_1}, \ldots, \sqrt{p_{n-1}})$

Published on 27 Dec 2019 - 23:52

List Question

Alternative proof for $[\mathbb{Q}(\sqrt{p},\sqrt{q}):\mathbb{Q}]=4$

Are coprime polynomials also coprime considered in the algebraic closure?

Questions about the proof of $a+b$ and $ab$ (transcendental/algebraic)

Minimal polynomial over $\mathbb{Q}$ (Computing)

$a+b$ and $ab$ are not both algebraic over $K$ (proof)

General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$

Maximal algebraic ordered field extensions of $\mathbb{Q}$

Proving equivalence between finite field extensions.

Finite field extension that is properly contained in a splitting field

Determine the splitting field (polynomial/degree)

Conditions for being an unramified extensions

A question on field and subfields

Simple question about Galois theory

Lang's definition of separability (solved)

Prove that $\sqrt{p_n}\not\in \mathbb{Q}(\sqrt{p_1}, \ldots, \sqrt{p_{n-1}})$

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