List questions from extension-field

Published on 09 Apr 2026 - 8:02

101

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Splitting field of a separable polynomial is also the splitting field of an irreducible separable polynomial

Published on 14 Apr 2026 - 10:36

103

Views

Degree of extension of root of a polynomial system

Published on 11 Apr 2026 - 5:03

63

Views

Question involving Galois Extension

Published on 12 Apr 2026 - 19:01

33

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Why $F(S)=\cup_{r=1}^{\infty} F(\alpha_1, \dots ,\alpha_r)$ instead of $F(S)=F(\alpha_1, \dots ,\alpha_r)$?

Published on 17 Apr 2026 - 1:49

26

Views

An example to explain the definition $\alpha \in \bar{F}$ is radical over $F.$

Published on 23 Apr 2026 - 16:32

176

Views

Non-isomorphicity of certain fields.

Published on 15 Apr 2026 - 11:08

78

Views

Some basic question about obtain minimal polynomial of algebraic element.

Published on 12 Apr 2026 - 5:52

58

Views

Adjoining subfields

Published on 13 Apr 2026 - 19:59

75

Views

Why would anyone think that $[E_1 E_2 : E_2]=[E_1:F]$?

Published on 16 Apr 2026 - 19:28

481

Views

Show that $\mathbb{Q}(\sqrt{a} + \sqrt{b}) = \mathbb{Q}(\sqrt{a}, \sqrt{b})$

Published on 15 Apr 2026 - 22:06

414

Views

Is it true that every algebraic extension $F$ of a field $E$ is generated by adding to $E$ an algebraic element?

Published on 13 Apr 2026 - 4:14

92

Views

Classification of cyclotomic extenson

Published on 12 Apr 2026 - 11:08

459

Views

Explaining field extensions

Published on 13 Apr 2026 - 2:17

635

Views

Proving K(x) is a simple extension of K(u)

Published on 14 Apr 2026 - 9:33

List Question

Relationship between modulus (absolute value) and algebraic norm.

Splitting field of a separable polynomial is also the splitting field of an irreducible separable polynomial

Degree of extension of root of a polynomial system

Question involving Galois Extension

Why $F(S)=\cup_{r=1}^{\infty} F(\alpha_1, \dots ,\alpha_r)$ instead of $F(S)=F(\alpha_1, \dots ,\alpha_r)$?

An example to explain the definition $\alpha \in \bar{F}$ is radical over $F.$

Non-isomorphicity of certain fields.

Some basic question about obtain minimal polynomial of algebraic element.

Adjoining subfields

Why would anyone think that $[E_1 E_2 : E_2]=[E_1:F]$?

Show that $\mathbb{Q}(\sqrt{a} + \sqrt{b}) = \mathbb{Q}(\sqrt{a}, \sqrt{b})$

Is it true that every algebraic extension $F$ of a field $E$ is generated by adding to $E$ an algebraic element?

Classification of cyclotomic extenson

Explaining field extensions

Proving K(x) is a simple extension of K(u)

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