List questions from field-theory

Published on 26 Mar 2026 - 4:30

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The ladder of the real closure of an ordered field

Published on 25 Mar 2026 - 7:44

91

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How to prove $ \left\{ t^2,t^3 \right\}$ equals the vanishing set of $y^2-x^3$?

Published on 30 Mar 2026 - 3:56

240

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Field Extensions and Injectivity

Published on 25 Mar 2026 - 4:35

504

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Proving that $\sqrt 3\not\in Q(\sqrt[4]2)$

Published on 29 Mar 2026 - 23:24

2.5k

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Is it true that $F$ is a field if and only if $F[X]$ is an Euclidean domain?

Published on 24 Nov 2018 - 3:52

168

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Determine $[K:\mathbb{Q}]$ and show that $Gal(K/\mathbb{Q})$ is non-abelian.

Published on 30 Mar 2026 - 5:32

34

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$n$th- roots of unit in a splitting field

Published on 29 Mar 2026 - 23:25

430

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$f(x)\in \mathbb F_p[X]$ irreducible. Then a splitting field for $f(x)$ has $p^n$ elements

Published on 27 Mar 2026 - 14:59

244

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Proof: $ { \mathbb{Q}[x] } / (x^2 +3x +1) \cong \mathbb{Q}(\sqrt{5}) $

Published on 25 Mar 2026 - 17:43

43

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Quadratic reciprocity for some fields

Published on 25 Nov 2018 - 3:12

411

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Show that $F[\alpha] = \{ f(\alpha): f(x) \in F[x]\}$ is a field iff $\alpha$ is algebraic over F

Published on 29 Mar 2026 - 23:27

181

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Number of elements in the ideal of Ring.

Published on 25 Mar 2026 - 16:08

104

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Finite Fields, Field Extensions, and Minimal Polynomials

Published on 30 Mar 2026 - 1:10

1.5k

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Finding the minimal polynomial for each algebraic element over $\mathbb{Q}$.

Published on 25 Nov 2018 - 19:55

List Question

Strategies for finding $[\mathbb{Q} (\sqrt{2} + \sqrt{3}) : \mathbb{Q} ]$

The ladder of the real closure of an ordered field

How to prove $ \left\{ t^2,t^3 \right\}$ equals the vanishing set of $y^2-x^3$?

Field Extensions and Injectivity

Proving that $\sqrt 3\not\in Q(\sqrt[4]2)$

Is it true that $F$ is a field if and only if $F[X]$ is an Euclidean domain?

Determine $[K:\mathbb{Q}]$ and show that $Gal(K/\mathbb{Q})$ is non-abelian.

$n$th- roots of unit in a splitting field

$f(x)\in \mathbb F_p[X]$ irreducible. Then a splitting field for $f(x)$ has $p^n$ elements

Proof: $ { \mathbb{Q}[x] } / (x^2 +3x +1) \cong \mathbb{Q}(\sqrt{5}) $

Quadratic reciprocity for some fields

Show that $F[\alpha] = \{ f(\alpha): f(x) \in F[x]\}$ is a field iff $\alpha$ is algebraic over F

Number of elements in the ideal of Ring.

Finite Fields, Field Extensions, and Minimal Polynomials

Finding the minimal polynomial for each algebraic element over $\mathbb{Q}$.

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