List questions from field-theory

Published on 14 Apr 2026 - 9:46

820

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Prove the polynomial ring and field isomorphisms

Published on 16 Apr 2026 - 4:48

112

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Calculating discriminant of elements of $\mathbb{Q}(a)$

Published on 10 May 2026 - 16:33

51

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Prove that the following is vector space

Published on 17 Apr 2026 - 5:26

645

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Show that $F((X))$ is a field and that $\mathbb Q((X))$ is the fraction field of $\mathbb Z[[X]]$.

Published on 14 Apr 2026 - 10:20

341

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Factorization of $X^{p^n}-X-c$ over $\mathbb{F}_{p^n}$

Published on 16 Apr 2026 - 13:58

318

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Fields and Galois theory.

Published on 12 Apr 2026 - 4:45

1.5k

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Generalisation of integers for infinite length?

Published on 12 Apr 2026 - 19:38

276

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Can the cubic be solved this way?

Published on 12 Apr 2026 - 2:04

95

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Minimal degree of polynomial which local-global principle is not effective

Published on 09 Apr 2026 - 3:52

104

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$\mathbb{C}$ is a $\mathbb{R}$ vector-space: problems with field embedding

Published on 13 Apr 2026 - 21:56

40

Views

why this is true in cyclic code?

Published on 15 Apr 2026 - 12:11

88

Views

Proof in field of quotients (form of elements)

Published on 11 Apr 2026 - 17:00

244

Views

Prime Field Extensions Equal or Intersection Base Field

Published on 13 Apr 2026 - 19:02

848

Views

Example of a finite field extension

Published on 14 Apr 2026 - 13:30

List Question

Ring of integers of $\mathbb{Q}(a)$

Prove the polynomial ring and field isomorphisms

Calculating discriminant of elements of $\mathbb{Q}(a)$

Prove that the following is vector space

Show that $F((X))$ is a field and that $\mathbb Q((X))$ is the fraction field of $\mathbb Z[[X]]$.

Factorization of $X^{p^n}-X-c$ over $\mathbb{F}_{p^n}$

Fields and Galois theory.

Generalisation of integers for infinite length?

Can the cubic be solved this way?

Minimal degree of polynomial which local-global principle is not effective

$\mathbb{C}$ is a $\mathbb{R}$ vector-space: problems with field embedding

why this is true in cyclic code?

Proof in field of quotients (form of elements)

Prime Field Extensions Equal or Intersection Base Field

Example of a finite field extension

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