List questions from extension-field

Published on 17 Apr 2026 - 12:25

73

Views

Extension elements always exist for field extensions?

Published on 14 Apr 2026 - 5:17

481

Views

Coprime degree of minimum polynomials

Published on 12 Apr 2026 - 10:11

538

Views

Element algebraic over field iff algebraic over field extension

Published on 14 Apr 2026 - 12:55

206

Views

What is $[\mathbb{Q}(i,\sqrt{2},\sqrt{3}):\mathbb{Q}]$?

Published on 16 Apr 2026 - 0:48

487

Views

Root field of $x^3+2x+1$ over $\mathbb{Z}_3$

Published on 13 Apr 2026 - 8:32

95

Views

Root field of $x^3+x^2+x+2$ over $\mathbb{Z}_3$

Published on 15 Apr 2026 - 12:03

198

Views

Field extension of complex root of cubic equation

Published on 12 Apr 2026 - 0:51

1k

Views

Splitting field is a splitting field for any root of irreducible polynomial

Published on 11 Apr 2026 - 22:01

1.9k

Views

Separability and tensor product of fields

Published on 14 Apr 2026 - 14:01

50

Views

Rotation on extension-field

Published on 12 Apr 2026 - 14:34

3.5k

Views

Intermediate fields of a field extension

Published on 14 Apr 2026 - 6:33

373

Views

Example where prime spectrum suits better than the maximal spectrum

Published on 14 Apr 2026 - 15:13

321

Views

How to check whether a $\mathbb{K}$-algebra homomorphism restricts to identity on $\mathbb{K}$

Published on 10 Apr 2026 - 0:13

69

Views

Determine element in a field extension

Published on 14 Apr 2026 - 23:39

List Question

Find basis of $\mathbb{Q}(\sqrt{2}+\sqrt[3]{4})$

Extension elements always exist for field extensions?

Coprime degree of minimum polynomials

Element algebraic over field iff algebraic over field extension

What is $[\mathbb{Q}(i,\sqrt{2},\sqrt{3}):\mathbb{Q}]$?

Root field of $x^3+2x+1$ over $\mathbb{Z}_3$

Root field of $x^3+x^2+x+2$ over $\mathbb{Z}_3$

Field extension of complex root of cubic equation

Splitting field is a splitting field for any root of irreducible polynomial

Separability and tensor product of fields

Rotation on extension-field

Intermediate fields of a field extension

Example where prime spectrum suits better than the maximal spectrum

How to check whether a $\mathbb{K}$-algebra homomorphism restricts to identity on $\mathbb{K}$

Determine element in a field extension

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