Question

An exercise about field extension

score 85 · Answer 1 · 2026-04-09 15:01:48

85

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An exercise about field extension

Published on 09 Apr 2026 - 15:01

score 35 · Answer 2 · 2026-04-14 06:03:12

35

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Does every field extension of a field containing irreducible polynomial have a root?

Published on 14 Apr 2026 - 6:03

score 78 · Answer 3 · 2026-04-12 22:29:37

78

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Is any algebraic extension a subfield of a spitting field?

Published on 12 Apr 2026 - 22:29

score 179 · Answer 4 · 2026-04-16 20:31:45

179

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Is there an isomorphism of $F[x]/\langle x^2+a\rangle$ to $F[x]/\langle x^2+x+b\rangle$ just as fields?

Published on 16 Apr 2026 - 20:31

score 817 · Answer 5 · 2026-04-14 12:08:03

817

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Basis and transcendental basis

Published on 14 Apr 2026 - 12:08

score 256 · Answer 6 · 2026-03-25 19:00:30

256

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Are there Olympiad problems that can be solved using split-complex numbers?

Published on 25 Mar 2026 - 19:00

score 177 · Answer 7 · 2026-04-17 07:40:31

177

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degree field extension by a power of transcendental element

Published on 17 Apr 2026 - 7:40

score 952 · Answer 8 · 2026-04-15 04:07:41

952

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A simple finite field extension only has finitely many intermediate fields

Published on 15 Apr 2026 - 4:07

score 70 · Answer 9 · 2026-04-16 16:01:31

70

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Find the degree of the normal closure $E$ of $F$ over $\mathbb Q$. What is the degree of $E$ over $\mathbb Q$?

Published on 16 Apr 2026 - 16:01

score 127 · Answer 10 · 2026-04-15 05:29:58

127

Views

Is $x$ an algebraic element over the field of rational functions $K(x)^p$?

Published on 15 Apr 2026 - 5:29

score 81 · Answer 11 · 2026-04-16 09:10:11

81

Views

Is every element of $\mathbb{R}$ a member of $\mathbb{Q}$ adjoined with finitely many members of its transcendence basis?

Published on 16 Apr 2026 - 9:10

score 184 · Answer 12 · 2026-04-12 08:46:43

184

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Field extension with infinite degree

Published on 12 Apr 2026 - 8:46

score 190 · Answer 13 · 2026-04-15 13:39:56

190

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Intermediate fields of the simple extension $\mathbb{C}(x)$

Published on 15 Apr 2026 - 13:39

score 530 · Answer 14 · 2026-04-16 05:18:34

530

Views

Solvability by radicals of a separable field of characteristic $p$

Published on 16 Apr 2026 - 5:18

score 98 · Answer 15 · 2026-04-14 22:35:35

98

Views

Calculating the degree of a splitting field of $f(x)=x^4-4x^3-4x^2+16x-8$ over $\mathbb{Q}$.

Published on 14 Apr 2026 - 22:35

List Question

An exercise about field extension

Does every field extension of a field containing irreducible polynomial have a root?

Is any algebraic extension a subfield of a spitting field?

Is there an isomorphism of $F[x]/\langle x^2+a\rangle$ to $F[x]/\langle x^2+x+b\rangle$ just as fields?

Basis and transcendental basis

Are there Olympiad problems that can be solved using split-complex numbers?

degree field extension by a power of transcendental element

A simple finite field extension only has finitely many intermediate fields

Find the degree of the normal closure $E$ of $F$ over $\mathbb Q$. What is the degree of $E$ over $\mathbb Q$?

Is $x$ an algebraic element over the field of rational functions $K(x)^p$?

Is every element of $\mathbb{R}$ a member of $\mathbb{Q}$ adjoined with finitely many members of its transcendence basis?

Field extension with infinite degree

Intermediate fields of the simple extension $\mathbb{C}(x)$

Solvability by radicals of a separable field of characteristic $p$

Calculating the degree of a splitting field of $f(x)=x^4-4x^3-4x^2+16x-8$ over $\mathbb{Q}$.

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