Question

Question about a proof: $U$ maximal among non-finitely generated ideals of $R$, then $U$ is a prime ideal.

score 61 · Answer 1 · 2021-12-21 23:47:55

61

Views

Question about a proof: $U$ maximal among non-finitely generated ideals of $R$, then $U$ is a prime ideal.

Published on 21 Dec 2021 - 23:47

score 54 · Answer 2 · 2021-12-22 01:40:55

54

Views

Question from the proof of the thread dealing with showing an ideal maximal in the set of ideals not intersecting multiplicative sets is prime.

Published on 22 Dec 2021 - 1:40

score 42 · Answer 3 · 2021-12-23 13:27:38

42

Views

If $P$ is a prime ideal in a commutative ring $R$ with unity, and $\{P\}$ is closed under the Zariski topology on $\text{Spec}R$, then $P$ is maximal.

Published on 23 Dec 2021 - 13:27

score 120 · Answer 4 · 2021-12-23 22:04:26

120

Views

How to turn elements of a ring $A$ into functions on $\text{Spec}A$?

Published on 23 Dec 2021 - 22:04

score 100 · Answer 5 · 2021-12-24 04:17:54

100

Views

(Unique) OR (unique + nontrivial) prime ideal

Published on 24 Dec 2021 - 4:17

score 155 · Answer 6 · 2026-03-27 21:55:47

155

Views

Support of module and faithfully flat base change

Published on 27 Mar 2026 - 21:55

score 201 · Answer 7 · 2026-03-25 15:57:27

201

Views

Exercise 4.2, Atiyah Macdonald

Published on 25 Mar 2026 - 15:57

score 378 · Answer 8 · 2026-04-01 16:15:24

378

Views

A prime ideal of a polynomial ring over a PID can be generated by two elements.

Published on 01 Apr 2026 - 16:15

score 173 · Answer 9 · 2026-04-01 07:13:58

173

Views

Exercise with localization and minimal primes

Published on 01 Apr 2026 - 7:13

score 117 · Answer 10 · 2026-03-29 14:59:11

117

Views

Question about a proof involving local rings: $R$ has exactly $3$ ideals, show that if $a,b\in I$ then $ab=0$

Published on 29 Mar 2026 - 14:59

score 142 · Answer 11 · 2026-04-01 07:15:39

142

Views

Characterization of maximal multiplicatively closed subsets

Published on 01 Apr 2026 - 7:15

score 47 · Answer 12 · 2022-01-03 16:22:25

47

Views

Is the ideal, prime? maximal? Is it principal?

Published on 03 Jan 2022 - 16:22

score 133 · Answer 13 · 2022-01-03 20:27:19

133

Views

Show that $R\cong R_P$, the ring of quotients of $R$ with respect to the multiplicative set $R-P$ if $R$ has exactly one prime ideal $P$.

Published on 03 Jan 2022 - 20:27

score 158 · Answer 14 · 2026-03-29 11:44:22

158

Views

Show that $(x^3+x+1)$ is prime in $\mathbb{Z}/(2)[x]$

Published on 29 Mar 2026 - 11:44

score 191 · Answer 15 · 2022-01-09 21:23:33

191

Views

Do the rings $\mathbb{Z}[x]$ or $\mathbb{Q}[x]$ have a quotient isomorphic to the field with 9 elements?

Published on 09 Jan 2022 - 21:23

List Question

Question about a proof: $U$ maximal among non-finitely generated ideals of $R$, then $U$ is a prime ideal.

Question from the proof of the thread dealing with showing an ideal maximal in the set of ideals not intersecting multiplicative sets is prime.

If $P$ is a prime ideal in a commutative ring $R$ with unity, and $\{P\}$ is closed under the Zariski topology on $\text{Spec}R$, then $P$ is maximal.

How to turn elements of a ring $A$ into functions on $\text{Spec}A$?

(Unique) OR (unique + nontrivial) prime ideal

Support of module and faithfully flat base change

Exercise 4.2, Atiyah Macdonald

A prime ideal of a polynomial ring over a PID can be generated by two elements.

Exercise with localization and minimal primes

Question about a proof involving local rings: $R$ has exactly $3$ ideals, show that if $a,b\in I$ then $ab=0$

Characterization of maximal multiplicatively closed subsets

Is the ideal, prime? maximal? Is it principal?

Show that $R\cong R_P$, the ring of quotients of $R$ with respect to the multiplicative set $R-P$ if $R$ has exactly one prime ideal $P$.

Show that $(x^3+x+1)$ is prime in $\mathbb{Z}/(2)[x]$

Do the rings $\mathbb{Z}[x]$ or $\mathbb{Q}[x]$ have a quotient isomorphic to the field with 9 elements?

Trending Questions

Popular # Hahtags

Popular Questions