Question

Prove that two polynomials $f,g \in k[X]$ have a common root in $\bar k$ iff $f,g$ have a common factor in $k[X])$.

score 1k · Answer 1 · 2026-03-26 18:51:51

1k

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Prove that two polynomials $f,g \in k[X]$ have a common root in $\bar k$ iff $f,g$ have a common factor in $k[X])$.

Published on 26 Mar 2026 - 18:51

score 1.3k · Answer 2 · 2026-03-26 22:53:27

1.3k

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Elements and structure of units in $\mathbb Q(\sqrt {-7})$

Published on 26 Mar 2026 - 22:53

score 2.9k · Answer 3 · 2026-03-26 22:58:00

2.9k

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Prime in $\mathbb Z [\sqrt{-5}]$ but not in $\mathbb Z [\sqrt{5}]$

Published on 26 Mar 2026 - 22:58

score 443 · Answer 4 · 2026-03-25 04:38:22

443

Views

Is this the (real) algebraic numbers?

Published on 25 Mar 2026 - 4:38

score 169 · Answer 5 · 2026-03-25 06:05:34

169

Views

Axiomatize purely transcendental field extension

Published on 25 Mar 2026 - 6:05

score 223 · Answer 6 · 2026-03-25 03:01:44

223

Views

Prime ideals in $\mathbb Z[\zeta_{18}]$?

Published on 25 Mar 2026 - 3:01

score 66 · Answer 7 · 2026-03-25 16:40:02

66

Views

Which of these principle ideals is maximal in $\mathbb{Z}[x]$?

Published on 25 Mar 2026 - 16:40

score 670 · Answer 8 · 2026-03-25 06:04:09

670

Views

Finitely generated extension of transcendence degree 1

Published on 25 Mar 2026 - 6:04

score 48 · Answer 9 · 2026-03-25 03:20:42

48

Views

$x^2-2$ is irreducible in $\mathbb{Q}[x]$ implies that $\mathbb{Q}[\sqrt{2}]$ is a field

Published on 25 Mar 2026 - 3:20

score 65 · Answer 10 · 2026-03-25 07:35:41

65

Views

Field generated and fraction field

Published on 25 Mar 2026 - 7:35

score 139 · Answer 11 · 2026-03-27 00:56:56

139

Views

Is $\mathbb{C}\otimes _{\mathbb{Z}} \mathbb{C}$ isomorphic to $\mathbb{C}\otimes _{\mathbb{Q}} \mathbb{C}$ as ring?

Published on 27 Mar 2026 - 0:56

score 41 · Answer 12 · 2018-03-19 12:18:06

41

Views

Is it true that $[L\lor L':L']=[L:L\cap L']$ in $\mathbb{C}$

Published on 19 Mar 2018 - 12:18

score 439 · Answer 13 · 2026-03-25 03:20:38

439

Views

Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?

Published on 25 Mar 2026 - 3:20

score 80 · Answer 14 · 2018-03-20 11:09:12

80

Views

Why is $\mathbb{Q}(\sqrt[4]{2})$ $\mathbb{Q}$-isomorpic to $\mathbb{Q}(i\sqrt[4]{2})$

Published on 20 Mar 2018 - 11:09

score 230 · Answer 15 · 2026-03-25 05:46:59

230

Views

Why is K the letter denoting fields?

Published on 25 Mar 2026 - 5:46

List Question

Prove that two polynomials $f,g \in k[X]$ have a common root in $\bar k$ iff $f,g$ have a common factor in $k[X])$.

Elements and structure of units in $\mathbb Q(\sqrt {-7})$

Prime in $\mathbb Z [\sqrt{-5}]$ but not in $\mathbb Z [\sqrt{5}]$

Is this the (real) algebraic numbers?

Axiomatize purely transcendental field extension

Prime ideals in $\mathbb Z[\zeta_{18}]$?

Which of these principle ideals is maximal in $\mathbb{Z}[x]$?

Finitely generated extension of transcendence degree 1

$x^2-2$ is irreducible in $\mathbb{Q}[x]$ implies that $\mathbb{Q}[\sqrt{2}]$ is a field

Field generated and fraction field

Is $\mathbb{C}\otimes _{\mathbb{Z}} \mathbb{C}$ isomorphic to $\mathbb{C}\otimes _{\mathbb{Q}} \mathbb{C}$ as ring?

Is it true that $[L\lor L':L']=[L:L\cap L']$ in $\mathbb{C}$

Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?

Why is $\mathbb{Q}(\sqrt[4]{2})$ $\mathbb{Q}$-isomorpic to $\mathbb{Q}(i\sqrt[4]{2})$

Why is K the letter denoting fields?

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