Question

software to compute the degree of the splitting field of a polynomial over $\mathbb{Q}$

score 680 · Answer 1 · 2026-03-25 08:10:56

680

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software to compute the degree of the splitting field of a polynomial over $\mathbb{Q}$

Published on 25 Mar 2026 - 8:10

score 381 · Answer 2 · 2026-04-13 11:21:26

381

Views

Necessary and Sufficient conditions for $F(a)=F[a]$? (Field Extension)

Published on 13 Apr 2026 - 11:21

score 580 · Answer 3 · 2026-04-14 01:15:35

580

Views

Example of infinite extension of $\mathbb{R}$?

Published on 14 Apr 2026 - 1:15

score 64 · Answer 4 · 2026-04-14 07:47:36

64

Views

Proof Verification: Field extension where every element is a product of elements of a certain form

Published on 14 Apr 2026 - 7:47

score 731 · Answer 5 · 2026-04-16 11:46:06

731

Views

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

Published on 16 Apr 2026 - 11:46

score 71 · Answer 6 · 2026-04-16 11:06:12

71

Views

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

Published on 16 Apr 2026 - 11:06

score 65 · Answer 7 · 2026-04-17 04:25:10

65

Views

Confusion in how to handle the "or both" part of If $x, y \in \mathbb{F}$, then if $x\cdot y = 0$, then $x=0$ or $y = 0$ (or both).

Published on 17 Apr 2026 - 4:25

score 59 · Answer 8 · 2026-04-15 18:10:18

59

Views

Prove that this is an equivalence relation

Published on 15 Apr 2026 - 18:10

score 130 · Answer 9 · 2026-04-13 05:06:08

130

Views

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

Published on 13 Apr 2026 - 5:06

score 68 · Answer 10 · 2026-04-15 22:47:58

68

Views

What is the dimension over $ \mathbb{C} $ of $ \mathbb{C} [X,Y] / ( Y^2 - X^2 , Y^2 + X^2 ) $?

Published on 15 Apr 2026 - 22:47

score 1.9k · Answer 11 · 2026-03-25 13:34:20

1.9k

Views

Does there exist a pair of infinite fields, the additive group of one isomorphic to the multiplicative group of the other?

Published on 25 Mar 2026 - 13:34

score 129 · Answer 12 · 2026-04-15 08:33:50

129

Views

Is $\Bbb Q[\sqrt{2}]$ a field?

Published on 15 Apr 2026 - 8:33

score 157 · Answer 13 · 2026-04-14 09:32:41

157

Views

Is the following proposition true or false?

Published on 14 Apr 2026 - 9:32

score 795 · Answer 14 · 2026-04-15 20:36:21

795

Views

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

Published on 15 Apr 2026 - 20:36

score 457 · Answer 15 · 2026-04-16 15:32:03

457

Views

$\mathbb{Q}[x]/ \langle α(x) \rangle$ if the polynomial is reducible

Published on 16 Apr 2026 - 15:32

List Question

software to compute the degree of the splitting field of a polynomial over $\mathbb{Q}$

Necessary and Sufficient conditions for $F(a)=F[a]$? (Field Extension)

Example of infinite extension of $\mathbb{R}$?

Proof Verification: Field extension where every element is a product of elements of a certain form

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 $k$.

Confusion in how to handle the "or both" part of If $x, y \in \mathbb{F}$, then if $x\cdot y = 0$, then $x=0$ or $y = 0$ (or both).

Prove that this is an equivalence relation

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

What is the dimension over $ \mathbb{C} $ of $ \mathbb{C} [X,Y] / ( Y^2 - X^2 , Y^2 + X^2 ) $?

Does there exist a pair of infinite fields, the additive group of one isomorphic to the multiplicative group of the other?

Is $\Bbb Q[\sqrt{2}]$ a field?

Is the following proposition true or false?

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

$\mathbb{Q}[x]/ \langle α(x) \rangle$ if the polynomial is reducible

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