Question

Does there exist a Noetherian domain (which is not a field) whose field of fractions is (isomorphic with) $\mathbb C$?

score 165 · Answer 1 · 2026-04-10 16:09:29

165

Views

Does there exist a Noetherian domain (which is not a field) whose field of fractions is (isomorphic with) $\mathbb C$?

Published on 10 Apr 2026 - 16:09

score 1.7k · Answer 2 · 2026-04-11 03:07:06

1.7k

Views

Is there a clever(er) way to construct a finite field with nine elements?

Published on 11 Apr 2026 - 3:07

score 122 · Answer 3 · 2026-04-13 18:46:36

122

Views

Degree theory of rational fractions over $ \mathbb{C} $.

Published on 13 Apr 2026 - 18:46

score 194 · Answer 4 · 2026-04-18 00:49:48

194

Views

Is $\mathbb{Z_5}[x]/ \langle x^2+3,3 \rangle$ a field?

Published on 18 Apr 2026 - 0:49

score 436 · Answer 5 · 2026-04-16 08:57:54

436

Views

Why is $\mathbb{Q}$ the minimal field that contains $0$ and $1$ ?

Published on 16 Apr 2026 - 8:57

score 100 · Answer 6 · 2026-04-16 12:06:28

100

Views

Prove it is a field and find the number of its elements

Published on 16 Apr 2026 - 12:06

score 520 · Answer 7 · 2026-04-14 18:07:00

520

Views

Is a prime subfield a set of integers?

Published on 14 Apr 2026 - 18:07

score 85 · Answer 8 · 2026-04-13 12:23:55

85

Views

Redefining multiplication so that $\mathbb{Z}$ is a field?

Published on 13 Apr 2026 - 12:23

score 76 · Answer 9 · 2026-04-12 11:52:39

76

Views

Field extension over the reals

Published on 12 Apr 2026 - 11:52

score 146 · Answer 10 · 2026-04-17 04:19:12

146

Views

$\mathbb{Q}[x,y]/\langle x-1,y-3 \rangle \cong \mathbb{Q}$

Published on 17 Apr 2026 - 4:19

score 203 · Answer 11 · 2026-04-15 23:11:45

203

Views

Every element of $\mathbb{R}[x,y]/\langle x,x^2+y^2+1 \rangle$ is unit

Published on 15 Apr 2026 - 23:11

score 787 · Answer 12 · 2026-04-15 15:53:55

787

Views

Smallest subfield of $\mathbb{C}$ containing $\sqrt[5]{2}$

Published on 15 Apr 2026 - 15:53

score 49 · Answer 13 · 2026-04-16 11:21:59

49

Views

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

Published on 16 Apr 2026 - 11:21

score 199 · Answer 14 · 2026-04-16 11:55:17

199

Views

Any field element $x \in L$ satisfies its own characteristic polynomial.

Published on 16 Apr 2026 - 11:55

score 43 · Answer 15 · 2026-04-15 12:00:27

43

Views

$\mathbb{C}^{n}$ vector space, $\mathbb{R}$ field, $\det(A) = 0 + bi$, $b \neq 0$, does this imply columns of the matrix are linearly independent?

Published on 15 Apr 2026 - 12:00

List Question

Does there exist a Noetherian domain (which is not a field) whose field of fractions is (isomorphic with) $\mathbb C$?

Is there a clever(er) way to construct a finite field with nine elements?

Degree theory of rational fractions over $ \mathbb{C} $.

Is $\mathbb{Z_5}[x]/ \langle x^2+3,3 \rangle$ a field?

Why is $\mathbb{Q}$ the minimal field that contains $0$ and $1$ ?

Prove it is a field and find the number of its elements

Is a prime subfield a set of integers?

Redefining multiplication so that $\mathbb{Z}$ is a field?

Field extension over the reals

$\mathbb{Q}[x,y]/\langle x-1,y-3 \rangle \cong \mathbb{Q}$

Every element of $\mathbb{R}[x,y]/\langle x,x^2+y^2+1 \rangle$ is unit

Smallest subfield of $\mathbb{C}$ containing $\sqrt[5]{2}$

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

Any field element $x \in L$ satisfies its own characteristic polynomial.

$\mathbb{C}^{n}$ vector space, $\mathbb{R}$ field, $\det(A) = 0 + bi$, $b \neq 0$, does this imply columns of the matrix are linearly independent?

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