Question

The field extension $\mathbb{C}/\mathbb{Q}$ is infinite

score 2.5k · Answer 1 · 2016-08-23 18:02:26

2.5k

Views

The field extension $\mathbb{C}/\mathbb{Q}$ is infinite

Published on 23 Aug 2016 - 18:02

score 50 · Answer 2 · 2016-08-24 10:23:54

50

Views

A field extension that is a finitely generated algebra is an algebraic extension

Published on 24 Aug 2016 - 10:23

score 156 · Answer 3 · 2016-08-24 15:32:06

156

Views

Equivalent conditions to "$P(x)$ is the minimal polynomial of $u$ over $K$"

Published on 24 Aug 2016 - 15:32

score 772 · Answer 4 · 2016-08-26 06:10:41

772

Views

$f(x) $ be the minimal polynomial of $a$ (algebraic element) over $\mathbb Q$ , let $b=f'(a) \in \mathbb Q(a)$ , then is $\mathbb Q(a)=\mathbb Q(b)$?

Published on 26 Aug 2016 - 6:10

score 179 · Answer 5 · 2026-03-25 14:21:22

179

Views

$\sqrt{-1} \in \mathbb Q(\sqrt{-3})$?

Published on 25 Mar 2026 - 14:21

score 46 · Answer 6 · 2016-09-02 09:30:47

46

Views

Relations between $f(X,Y)$ such that $f(a,b)=0$ and minimal polynomials of $a$ and $b$

Published on 02 Sep 2016 - 9:30

score 728 · Answer 7 · 2016-09-05 16:23:10

728

Views

If $b$ is algebraic over a finite extension $K$ of $F$ then $[K(b):K]\mid [F(b):F]$

Published on 05 Sep 2016 - 16:23

score 68 · Answer 8 · 2016-09-05 18:35:54

68

Views

Is it true that $k[\alpha,\beta]=k(\alpha,\beta)$, $\alpha$ and $\beta$ are algebraic over $k$.

Published on 05 Sep 2016 - 18:35

score 127 · Answer 9 · 2016-09-07 09:30:40

127

Views

Trascendence degree of the field of fractions of $\mathcal{O}(\mathbb{C})$ over $\mathbb{C}$

Published on 07 Sep 2016 - 9:30

score 154 · Answer 10 · 2016-09-08 12:28:52

154

Views

Is the following proposition true or false?

Published on 08 Sep 2016 - 12:28

score 793 · Answer 11 · 2026-03-25 13:13:31

793

Views

Generalization of Kronecker–Weber theorem: is an abelian extension always cyclotomic?

Published on 25 Mar 2026 - 13:13

score 256 · Answer 12 · 2016-09-10 20:26:24

256

Views

Why is $\mathbb Q(\sqrt 2+\sqrt 3)=\mathbb Q(\sqrt2,\sqrt 3)$?

Published on 10 Sep 2016 - 20:26

score 251 · Answer 13 · 2026-03-27 00:38:54

251

Views

The splitting field of $p(x)=x^4+ax^2+b$ over $F$ is $F[x]/\langle p(x)\rangle$

Published on 27 Mar 2026 - 0:38

score 3.9k · Answer 14 · 2026-03-31 05:05:25

3.9k

Views

Showing isomorphism of field extensions

Published on 31 Mar 2026 - 5:05

score 49 · Answer 15 · 2026-04-03 14:08:08

49

Views

Factor $X^5+6X^3+15X^2+3$ in $\mathbb{Q}\left (\sqrt{-3},\sqrt{-2}\right )\left [X\right ]$?

Published on 03 Apr 2026 - 14:08

List Question

The field extension $\mathbb{C}/\mathbb{Q}$ is infinite

A field extension that is a finitely generated algebra is an algebraic extension

Equivalent conditions to "$P(x)$ is the minimal polynomial of $u$ over $K$"

$f(x) $ be the minimal polynomial of $a$ (algebraic element) over $\mathbb Q$ , let $b=f'(a) \in \mathbb Q(a)$ , then is $\mathbb Q(a)=\mathbb Q(b)$?

$\sqrt{-1} \in \mathbb Q(\sqrt{-3})$?

Relations between $f(X,Y)$ such that $f(a,b)=0$ and minimal polynomials of $a$ and $b$

If $b$ is algebraic over a finite extension $K$ of $F$ then $[K(b):K]\mid [F(b):F]$

Is it true that $k[\alpha,\beta]=k(\alpha,\beta)$, $\alpha$ and $\beta$ are algebraic over $k$.

Trascendence degree of the field of fractions of $\mathcal{O}(\mathbb{C})$ over $\mathbb{C}$

Is the following proposition true or false?

Generalization of Kronecker–Weber theorem: is an abelian extension always cyclotomic?

Why is $\mathbb Q(\sqrt 2+\sqrt 3)=\mathbb Q(\sqrt2,\sqrt 3)$?

The splitting field of $p(x)=x^4+ax^2+b$ over $F$ is $F[x]/\langle p(x)\rangle$

Showing isomorphism of field extensions

Factor $X^5+6X^3+15X^2+3$ in $\mathbb{Q}\left (\sqrt{-3},\sqrt{-2}\right )\left [X\right ]$?

Trending Questions

Popular # Hahtags

Popular Questions