Question

Problem related to Field Extension

score 27 · Answer 1 · 2026-04-11 02:26:45

27

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Problem related to Field Extension

Published on 11 Apr 2026 - 2:26

score 887 · Answer 2 · 2026-04-17 03:42:16

887

Views

Determine the intermediate fields of $\mathbb{Q}(\zeta_{20})$

Published on 17 Apr 2026 - 3:42

score 2.8k · Answer 3 · 2026-04-17 12:03:16

2.8k

Views

Find a basis of $\mathbb{Q}(\sqrt{2}, \sqrt[3]{2})$ over $\mathbb{Q}$

Published on 17 Apr 2026 - 12:03

score 112 · Answer 4 · 2026-04-16 20:04:33

112

Views

$[F:\mathbb{Q}]$ where $F$ is splitting field over $\mathbb{Q}$ of $f = x^{3} + x^{2} + 1$

Published on 16 Apr 2026 - 20:04

score 35 · Answer 5 · 2026-04-15 11:22:38

35

Views

Prime factorization correspondence in simple extensions.

Published on 15 Apr 2026 - 11:22

score 118 · Answer 6 · 2026-04-16 13:51:33

118

Views

Simple field extension's endomorphism is trivial?

Published on 16 Apr 2026 - 13:51

score 42 · Answer 7 · 2026-04-16 12:12:44

42

Views

Bijection between $\text{Hom}(E/K,C/K)$ and $\text{Hom}(F/K,C/K)\times \text{Hom}(E/F,C/F)$

Published on 16 Apr 2026 - 12:12

score 209 · Answer 8 · 2026-04-12 12:14:21

209

Views

degree of fixed extension of the rational function field

Published on 12 Apr 2026 - 12:14

score 218 · Answer 9 · 2026-04-16 06:15:09

218

Views

Prove that $\mathbb{Q}(\sqrt{a}+\sqrt[3]{b}) = \mathbb{Q}(\sqrt{a}, \sqrt[3]{b})$ without Galois theory

Published on 16 Apr 2026 - 6:15

score 49 · Answer 10 · 2026-04-17 04:37:19

49

Views

Expression for the element $(a+u)^{-1}$ in the extension field $G = F(u)$, where $u$ is a root of $x^{2}+px +q$ over a field $F$

Published on 17 Apr 2026 - 4:37

score 33 · Answer 11 · 2026-04-14 20:53:53

33

Views

Existence of a field extension such that for any natural number $n$ ,

Published on 14 Apr 2026 - 20:53

score 495 · Answer 12 · 2026-04-12 06:58:54

495

Views

Radical Tower implies Solvability by Radicals

Published on 12 Apr 2026 - 6:58

score 153 · Answer 13 · 2026-04-12 23:18:14

153

Views

Dimension of a splitting field over a field $K$

Published on 12 Apr 2026 - 23:18

score 67 · Answer 14 · 2026-04-15 16:06:00

67

Views

For $w \in F(u_{i},u_{2}, \cdots, u_{n})$ for each $u_{i}$ algebraic, prove degree of $w$ over $F$ is $\leq$ the product of the degrees

Published on 15 Apr 2026 - 16:06

score 2.2k · Answer 15 · 2026-04-13 16:45:36

2.2k

Views

Algebraically closed field extension can be not algebraic?

Published on 13 Apr 2026 - 16:45

List Question

Problem related to Field Extension

Determine the intermediate fields of $\mathbb{Q}(\zeta_{20})$

Find a basis of $\mathbb{Q}(\sqrt{2}, \sqrt[3]{2})$ over $\mathbb{Q}$

$[F:\mathbb{Q}]$ where $F$ is splitting field over $\mathbb{Q}$ of $f = x^{3} + x^{2} + 1$

Prime factorization correspondence in simple extensions.

Simple field extension's endomorphism is trivial?

Bijection between $\text{Hom}(E/K,C/K)$ and $\text{Hom}(F/K,C/K)\times \text{Hom}(E/F,C/F)$

degree of fixed extension of the rational function field

Prove that $\mathbb{Q}(\sqrt{a}+\sqrt[3]{b}) = \mathbb{Q}(\sqrt{a}, \sqrt[3]{b})$ without Galois theory

Expression for the element $(a+u)^{-1}$ in the extension field $G = F(u)$, where $u$ is a root of $x^{2}+px +q$ over a field $F$

Existence of a field extension such that for any natural number $n$ ,

Radical Tower implies Solvability by Radicals

Dimension of a splitting field over a field $K$

For $w \in F(u_{i},u_{2}, \cdots, u_{n})$ for each $u_{i}$ algebraic, prove degree of $w$ over $F$ is $\leq$ the product of the degrees

Algebraically closed field extension can be not algebraic?

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