Question

Finding the smallest field containing multivariate polynomial evaluations of the roots of an irreducible polynomial

score 46 · Answer 1 · 2026-02-23 01:23:37

46

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Finding the smallest field containing multivariate polynomial evaluations of the roots of an irreducible polynomial

Published on 23 Feb 2026 - 1:23

score 461 · Answer 2 · 2018-08-04 10:31:23

461

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Show that $\mathbb{Q} (\zeta_3 \sqrt[3]{2}) \neq \mathbb{Q}(\zeta_3^2 \sqrt[3]{2})$.

Published on 04 Aug 2018 - 10:31

score 73 · Answer 3 · 2026-03-26 22:13:19

73

Views

I don't understand How to do Extension field

Published on 26 Mar 2026 - 22:13

score 320 · Answer 4 · 2018-08-04 16:01:54

320

Views

Automorphisms of Finite Field Extension

Published on 04 Aug 2018 - 16:01

score 439 · Answer 5 · 2026-03-26 22:16:06

439

Views

Degree of finite field extension by adjoining root of minimal polynomial

Published on 26 Mar 2026 - 22:16

score 827 · Answer 6 · 2026-03-27 00:10:04

827

Views

Galois Theory by Rotman, Exercise 60, a field of four elements by using Kronecker's theorem and adjoining a root of $x^4-x$ to $\Bbb Z_2$

Published on 27 Mar 2026 - 0:10

score 76 · Answer 7 · 2018-08-05 18:31:24

76

Views

Constructing a new monogenic extension of fields

Published on 05 Aug 2018 - 18:31

score 46 · Answer 8 · 2018-08-06 08:21:11

46

Views

Does $K \cong K_0$ and $F \cong F_0$ imply $[K : F] = [K_0 : F_0]$?

Published on 06 Aug 2018 - 8:21

score 29 · Answer 9 · 2026-03-27 11:46:32

29

Views

Existence of only one extension

Published on 27 Mar 2026 - 11:46

score 51 · Answer 10 · 2018-08-07 04:01:43

51

Views

Methods of showing Field Extensions are equal

Published on 07 Aug 2018 - 4:01

score 73 · Answer 11 · 2026-03-27 10:08:24

73

Views

Elements over transcendental extension

Published on 27 Mar 2026 - 10:08

score 268 · Answer 12 · 2018-08-08 20:33:13

268

Views

Constant Term of a Monic Polynomial in $\mathbb{Z}[x]$ Is Divisible by 3

Published on 08 Aug 2018 - 20:33

score 265 · Answer 13 · 2026-03-27 13:20:02

265

Views

Galois extension in $\mathbb{C}$

Published on 27 Mar 2026 - 13:20

score 395 · Answer 14 · 2026-03-27 13:20:12

395

Views

Galois group in $\mathbb{C}$

Published on 27 Mar 2026 - 13:20

score 69 · Answer 15 · 2018-08-10 14:45:22

69

Views

There exist $y \in K$ and $b \in E \setminus F$ such that $\min(y,E)(X) = X^3-b$ in a concrete fields $F \leq E \leq K$

Published on 10 Aug 2018 - 14:45

List Question

Finding the smallest field containing multivariate polynomial evaluations of the roots of an irreducible polynomial

Show that $\mathbb{Q} (\zeta_3 \sqrt[3]{2}) \neq \mathbb{Q}(\zeta_3^2 \sqrt[3]{2})$.

I don't understand How to do Extension field

Automorphisms of Finite Field Extension

Degree of finite field extension by adjoining root of minimal polynomial

Galois Theory by Rotman, Exercise 60, a field of four elements by using Kronecker's theorem and adjoining a root of $x^4-x$ to $\Bbb Z_2$

Constructing a new monogenic extension of fields

Does $K \cong K_0$ and $F \cong F_0$ imply $[K : F] = [K_0 : F_0]$?

Existence of only one extension

Methods of showing Field Extensions are equal

Elements over transcendental extension

Constant Term of a Monic Polynomial in $\mathbb{Z}[x]$ Is Divisible by 3

Galois extension in $\mathbb{C}$

Galois group in $\mathbb{C}$

There exist $y \in K$ and $b \in E \setminus F$ such that $\min(y,E)(X) = X^3-b$ in a concrete fields $F \leq E \leq K$

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