Question

Find the dimension and a basis of the given extension field $\mathbb{Q} (\sqrt[3]{2}, \sqrt{3})$ of $\mathbb{Q}$.

score 106 · Answer 1 · 2019-12-11 16:25:20

106

Views

Find the dimension and a basis of the given extension field $\mathbb{Q} (\sqrt[3]{2}, \sqrt{3})$ of $\mathbb{Q}$.

Published on 11 Dec 2019 - 16:25

score 352 · Answer 2 · 2019-12-11 23:45:54

352

Views

If $r$ and $s$ are nonzero, prove that $\mathbb{Q}(\sqrt{r})=\mathbb{Q}(\sqrt{s})$ if and only if $r=t^2s$ for some $t\in \mathbb{Q}$.

Published on 11 Dec 2019 - 23:45

score 36 · Answer 3 · 2019-12-12 17:18:35

36

Views

Find all sub-fields of $\mathbb{Q}(\sqrt[4]{5},i)$

Published on 12 Dec 2019 - 17:18

score 295 · Answer 4 · 2019-12-12 19:48:06

295

Views

Is the extension $\mathbb{Q} \left( \sqrt{2}, \sqrt{3}, \sqrt{5} \right)$ simple?

Published on 12 Dec 2019 - 19:48

score 118 · Answer 5 · 2026-03-26 14:28:04

118

Views

Explanation about a theorem from Basic Algebra I, Jacobson

Published on 26 Mar 2026 - 14:28

score 139 · Answer 6 · 2019-12-14 06:10:45

139

Views

Example of non splitting finite extension of characteristic $p$.

Published on 14 Dec 2019 - 6:10

score 226 · Answer 7 · 2019-12-14 11:50:33

226

Views

$\mathbb Q(2^{1/3}+3^{1/3})=\mathbb Q(2^{1/3},3^{1/3})$?

Published on 14 Dec 2019 - 11:50

score 655 · Answer 8 · 2019-12-14 23:09:10

655

Views

Simple transcendental field extensions

Published on 14 Dec 2019 - 23:09

score 93 · Answer 9 · 2026-03-26 07:58:21

93

Views

Transcendental numbers (field extension/sum/product)

Published on 26 Mar 2026 - 7:58

score 140 · Answer 10 · 2026-03-29 19:27:03

140

Views

Showing that $[\mathbb{Q}(\sqrt{p},\sqrt{q}):\mathbb{Q}]=4$

Published on 29 Mar 2026 - 19:27

score 490 · Answer 11 · 2026-03-26 14:42:07

490

Views

Splitting field of $x^4 + 4$ over $\mathbb{Q}$

Published on 26 Mar 2026 - 14:42

score 148 · Answer 12 · 2026-03-29 21:22:29

148

Views

Computing the minimal polynomial (field extension)

Published on 29 Mar 2026 - 21:22

score 36 · Answer 13 · 2019-12-17 18:52:21

36

Views

How to prove $L(\alpha)/K(\alpha)$ is algebraic given $L/K$ is algebraic?

Published on 17 Dec 2019 - 18:52

score 88 · Answer 14 · 2019-12-17 23:29:44

88

Views

Minimal polynomial with $f(\alpha)=0$

Published on 17 Dec 2019 - 23:29

score 34 · Answer 15 · 2026-03-29 10:12:18

34

Views

Intersection of function fields

Published on 29 Mar 2026 - 10:12

List Question

Find the dimension and a basis of the given extension field $\mathbb{Q} (\sqrt[3]{2}, \sqrt{3})$ of $\mathbb{Q}$.

If $r$ and $s$ are nonzero, prove that $\mathbb{Q}(\sqrt{r})=\mathbb{Q}(\sqrt{s})$ if and only if $r=t^2s$ for some $t\in \mathbb{Q}$.

Find all sub-fields of $\mathbb{Q}(\sqrt[4]{5},i)$

Is the extension $\mathbb{Q} \left( \sqrt{2}, \sqrt{3}, \sqrt{5} \right)$ simple?

Explanation about a theorem from Basic Algebra I, Jacobson

Example of non splitting finite extension of characteristic $p$.

$\mathbb Q(2^{1/3}+3^{1/3})=\mathbb Q(2^{1/3},3^{1/3})$?

Simple transcendental field extensions

Transcendental numbers (field extension/sum/product)

Showing that $[\mathbb{Q}(\sqrt{p},\sqrt{q}):\mathbb{Q}]=4$

Splitting field of $x^4 + 4$ over $\mathbb{Q}$

Computing the minimal polynomial (field extension)

How to prove $L(\alpha)/K(\alpha)$ is algebraic given $L/K$ is algebraic?

Minimal polynomial with $f(\alpha)=0$

Intersection of function fields

Trending Questions

Popular # Hahtags

Popular Questions