List questions from field-theory

Published on 25 Mar 2026 - 19:24

32

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Compute the Galois group of L over K

Published on 28 Mar 2026 - 0:56

187

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Showing the irreducibility of $x^8 - 60 x^6 + 1160 x^4 - 7800 x^2 + 8836$ in $\mathbb{Q}[x]$

Published on 26 Mar 2026 - 0:53

146

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Why must an automorphism of an extension of $\mathbb{Q}$ send 1 to a rational number?

Published on 30 Mar 2026 - 9:42

404

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Example of an infinite simple extension.

Published on 30 Mar 2026 - 9:41

72

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How to find a basis of $\Bbb R(t)$ over $\Bbb R$?

Published on 25 Mar 2026 - 3:24

267

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What is the minimal polynomial of $\sqrt{3+4i}+\sqrt{3-4i}$ over $\mathbb{Q}$?

Published on 30 Mar 2026 - 15:45

472

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Showing existence of irreducible polynomial of degree 3 in $\mathbb{F}_p$

Published on 04 Apr 2026 - 4:40

154

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Field extensions and Intermediate Rings

Published on 04 Apr 2026 - 4:34

202

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find all algebraic elements of $\mathbb{Q}(\pi)$ over $\mathbb{Q}(\pi^2 -2\pi +5)$

Published on 13 Jan 2019 - 13:17

129

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Algebraic Field Extensions and Irreducible Polynomials

Published on 26 Mar 2026 - 12:13

195

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Is this a counterexample?

Published on 26 Mar 2026 - 22:58

95

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Proof verification: Proving or disproving that $(\Bbb R^+, \oplus, \otimes)$ as defined is a field

Published on 14 Jan 2019 - 5:36

232

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Does there exist an automorphism of $\mathbb{C}$ that does not keep $\mathbb{R}$ fixed?

Published on 25 Mar 2026 - 18:47

205

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Irrationality of $(a_1+\sqrt{b_1})(a_2+\sqrt{b_2})$

Published on 28 Mar 2026 - 13:42

List Question

Degree of splitting fields

Compute the Galois group of L over K

Showing the irreducibility of $x^8 - 60 x^6 + 1160 x^4 - 7800 x^2 + 8836$ in $\mathbb{Q}[x]$

Why must an automorphism of an extension of $\mathbb{Q}$ send 1 to a rational number?

Example of an infinite simple extension.

How to find a basis of $\Bbb R(t)$ over $\Bbb R$?

What is the minimal polynomial of $\sqrt{3+4i}+\sqrt{3-4i}$ over $\mathbb{Q}$?

Showing existence of irreducible polynomial of degree 3 in $\mathbb{F}_p$

Field extensions and Intermediate Rings

find all algebraic elements of $\mathbb{Q}(\pi)$ over $\mathbb{Q}(\pi^2 -2\pi +5)$

Algebraic Field Extensions and Irreducible Polynomials

Is this a counterexample?

Proof verification: Proving or disproving that $(\Bbb R^+, \oplus, \otimes)$ as defined is a field

Does there exist an automorphism of $\mathbb{C}$ that does not keep $\mathbb{R}$ fixed?

Irrationality of $(a_1+\sqrt{b_1})(a_2+\sqrt{b_2})$

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