Question

In any commutative ring with unity, every prime ideal is finitely generated implies every ideal is finitely generated; can it be prove without A.C.?

score 377 · Answer 1 · 2026-04-12 16:46:22

377

Views

In any commutative ring with unity, every prime ideal is finitely generated implies every ideal is finitely generated; can it be prove without A.C.?

Published on 12 Apr 2026 - 16:46

score 207 · Answer 2 · 2026-04-12 12:28:48

207

Views

In every ring with unity satisfying ACC, every ideal is finitely generated; can we prove it without assuming Axiom of choice?

Published on 12 Apr 2026 - 12:28

score 63 · Answer 3 · 2026-04-11 15:23:55

63

Views

Question about ideals

Published on 11 Apr 2026 - 15:23

score 525 · Answer 4 · 2026-04-11 22:47:12

525

Views

Further examples of Principal Ideal Domain that are not Euclidean Domains

Published on 11 Apr 2026 - 22:47

score 858 · Answer 5 · 2026-04-03 01:34:28

858

Views

All prime ideals are maximal - Counterexample

Published on 03 Apr 2026 - 1:34

score 2.9k · Answer 6 · 2026-04-12 01:03:48

2.9k

Views

Show that $R/(I \cap J) \cong (R/I) \times (R/J) $

Published on 12 Apr 2026 - 1:03

score 229 · Answer 7 · 2026-04-08 16:58:52

229

Views

Ideal in $\mathbb Z[x]$ which is not two-generated

Published on 08 Apr 2026 - 16:58

score 128 · Answer 8 · 2015-04-12 19:18:45

128

Views

Maximal ideal of $\mathbb{R}[x]$

Published on 12 Apr 2015 - 19:18

score 833 · Answer 9 · 2026-03-25 07:45:50

833

Views

Show that the ring of integers $A$ of the cubic field $\mathbb Q[x]$ with $x^3=2$ is principal.

Published on 25 Mar 2026 - 7:45

score 822 · Answer 10 · 2026-04-03 01:33:36

822

Views

True or false question about polynomial ring

Published on 03 Apr 2026 - 1:33

score 2.3k · Answer 11 · 2015-04-13 21:14:01

2.3k

Views

Are all prime ideals in $\mathbb Z[\sqrt{-5}]$ of the form $\langle c, a + b \sqrt{-5} \rangle$?

Published on 13 Apr 2015 - 21:14

score 1k · Answer 12 · 2026-03-27 16:21:44

1k

Views

If every maximal ideal is finitely generated is the ring Noetherian?

Published on 27 Mar 2026 - 16:21

score 899 · Answer 13 · 2026-04-12 03:22:56

899

Views

Is it true that an integral domain $R$ is a UFD if and only if intersection of any two principal ideals of $R$ is principal ?

Published on 12 Apr 2026 - 3:22

score 3.9k · Answer 14 · 2026-04-03 01:39:16

3.9k

Views

How can I verify that the ideal $(x^2-zw, z^2-yw, y^3-xw, w^3-xy^2z)$ is prime in $\mathbb Q[x,y,z,w]$?

Published on 03 Apr 2026 - 1:39

score 140 · Answer 15 · 2015-04-14 14:46:39

140

Views

Let I be an unmixed radical ideal of R. then (I:x) is unmixed

Published on 14 Apr 2015 - 14:46

List Question

In any commutative ring with unity, every prime ideal is finitely generated implies every ideal is finitely generated; can it be prove without A.C.?

In every ring with unity satisfying ACC, every ideal is finitely generated; can we prove it without assuming Axiom of choice?

Question about ideals

Further examples of Principal Ideal Domain that are not Euclidean Domains

All prime ideals are maximal - Counterexample

Show that $R/(I \cap J) \cong (R/I) \times (R/J) $

Ideal in $\mathbb Z[x]$ which is not two-generated

Maximal ideal of $\mathbb{R}[x]$

Show that the ring of integers $A$ of the cubic field $\mathbb Q[x]$ with $x^3=2$ is principal.

True or false question about polynomial ring

Are all prime ideals in $\mathbb Z[\sqrt{-5}]$ of the form $\langle c, a + b \sqrt{-5} \rangle$?

If every maximal ideal is finitely generated is the ring Noetherian?

Is it true that an integral domain $R$ is a UFD if and only if intersection of any two principal ideals of $R$ is principal ?

How can I verify that the ideal $(x^2-zw, z^2-yw, y^3-xw, w^3-xy^2z)$ is prime in $\mathbb Q[x,y,z,w]$?

Let I be an unmixed radical ideal of R. then (I:x) is unmixed

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