Question

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

score 651 · Answer 1 · 2019-02-24 00:03:00

651

Views

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

Published on 24 Feb 2019 - 0:03

score 78 · Answer 2 · 2026-03-25 06:00:23

78

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

Published on 25 Mar 2026 - 6:00

score 188 · Answer 3 · 2019-03-10 02:13:35

188

Views

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

Published on 10 Mar 2019 - 2:13

score 65 · Answer 4 · 2019-03-23 13:13:25

65

Views

Principal ideal in an integral domain

Published on 23 Mar 2019 - 13:13

score 714 · Answer 5 · 2019-03-26 17:49:22

714

Views

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 26 Mar 2019 - 17:49

score 131 · Answer 6 · 2019-04-17 09:35:55

131

Views

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

Published on 17 Apr 2019 - 9:35

score 237 · Answer 7 · 2019-04-27 13:08:39

237

Views

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

Published on 27 Apr 2019 - 13:08

score 58 · Answer 8 · 2019-05-04 17:05:25

58

Views

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

Published on 04 May 2019 - 17:05

score 164 · Answer 9 · 2019-05-06 19:18:48

164

Views

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

Published on 06 May 2019 - 19:18

score 176 · Answer 10 · 2019-05-13 18:36:19

176

Views

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

Published on 13 May 2019 - 18:36

score 53 · Answer 11 · 2019-05-22 14:08:39

53

Views

How to calculate a double integral

Published on 22 May 2019 - 14:08

score 597 · Answer 12 · 2019-05-26 21:14:28

597

Views

Show that this domain is integrally closed

Published on 26 May 2019 - 21:14

score 40 · Answer 13 · 2019-06-11 00:01:15

40

Views

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

Published on 11 Jun 2019 - 0:01

score 88 · Answer 14 · 2019-06-24 22:22:14

88

Views

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

Published on 24 Jun 2019 - 22:22

score 1.7k · Answer 15 · 2019-07-10 14:40:06

1.7k

Views

How to prove a set is an integral domain?

Published on 10 Jul 2019 - 14:40

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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