Question

Prove $(F/R) \otimes_R (F/R)=0$ for $R$ an integral domain and $F$ its field of fractions

score 654 · Answer 1 · 2026-04-13 10:33:33

654

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Prove $(F/R) \otimes_R (F/R)=0$ for $R$ an integral domain and $F$ its field of fractions

Published on 13 Apr 2026 - 10:33

score 81 · Answer 2 · 2026-05-10 14:59:44

81

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Group algebra is domain iff doesn't contain nonzero element whose square is 0

Published on 10 May 2026 - 14:59

score 191 · Answer 3 · 2026-04-08 20:12:19

191

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The localization of the ring $\mathbb{Z} \times \mathbb{Z}$ at every prime ideal is an integral domain

Published on 08 Apr 2026 - 20:12

score 68 · Answer 4 · 2026-04-11 05:03:52

68

Views

Principal ideal in an integral domain

Published on 11 Apr 2026 - 5:03

score 717 · Answer 5 · 2026-04-12 16:01:15

717

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An Ideal I of $ \mathbb Z[\sqrt 3]$ generated by an integer prime, such that $\mathbb Z[ \sqrt 3]/I$ is not an integral domain.

Published on 12 Apr 2026 - 16:01

score 134 · Answer 6 · 2026-04-13 05:21:38

134

Views

Is this proof of a irreducibility criterion in an integral domain correct?

Published on 13 Apr 2026 - 5:21

score 239 · Answer 7 · 2026-04-13 20:33:25

239

Views

$\deg(fg)$ in a non integral domain ring

Published on 13 Apr 2026 - 20:33

score 61 · Answer 8 · 2026-04-13 18:17:59

61

Views

By showing that $R/I$ is an integral domain, deduce that it's a field.

Published on 13 Apr 2026 - 18:17

score 167 · Answer 9 · 2026-04-14 15:51:06

167

Views

How do I find the generator $(g)$ that generates $(29, \sqrt{-5} ± 13)$

Published on 14 Apr 2026 - 15:51

score 180 · Answer 10 · 2026-05-10 15:00:48

180

Views

Sufficient conditions for an element to be a unit in a euclidean domain

Published on 10 May 2026 - 15:00

score 57 · Answer 11 · 2026-04-09 07:19:59

57

Views

How to calculate a double integral

Published on 09 Apr 2026 - 7:19

score 600 · Answer 12 · 2026-04-14 23:09:04

600

Views

Show that this domain is integrally closed

Published on 14 Apr 2026 - 23:09

score 43 · Answer 13 · 2026-04-11 14:37:22

43

Views

$R[1/a] \cap R[1/b] = R$ for domain $R$ with $(a, b) = R$.

Published on 11 Apr 2026 - 14:37

score 91 · Answer 14 · 2026-04-13 22:59:33

91

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How to prove that $\Bbb R[x]/\langle x^5+x-3\rangle$ is not an integral domain?

Published on 13 Apr 2026 - 22:59

score 1.7k · Answer 15 · 2026-04-09 14:53:15

1.7k

Views

How to prove a set is an integral domain?

Published on 09 Apr 2026 - 14:53

List Question

Prove $(F/R) \otimes_R (F/R)=0$ for $R$ an integral domain and $F$ its field of fractions

Group algebra is domain iff doesn't contain nonzero element whose square is 0

The localization of the ring $\mathbb{Z} \times \mathbb{Z}$ at every prime ideal is an integral domain

Principal ideal in an integral domain

An Ideal I of $ \mathbb Z[\sqrt 3]$ generated by an integer prime, such that $\mathbb Z[ \sqrt 3]/I$ is not an integral domain.

Is this proof of a irreducibility criterion in an integral domain correct?

$\deg(fg)$ in a non integral domain ring

By showing that $R/I$ is an integral domain, deduce that it's a field.

How do I find the generator $(g)$ that generates $(29, \sqrt{-5} ± 13)$

Sufficient conditions for an element to be a unit in a euclidean domain

How to calculate a double integral

Show that this domain is integrally closed

$R[1/a] \cap R[1/b] = R$ for domain $R$ with $(a, b) = R$.

How to prove that $\Bbb R[x]/\langle x^5+x-3\rangle$ is not an integral domain?

How to prove a set is an integral domain?

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