Question

$2$-dimensional Noetherian integrally closed domains are Cohen-Macaulay

score 662 · Answer 1 · 2026-05-10 19:35:50

662

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$2$-dimensional Noetherian integrally closed domains are Cohen-Macaulay

Published on 10 May 2026 - 19:35

score 202 · Answer 2 · 2026-04-15 14:11:05

202

Views

Prove that if $\mathrm D$ is integral domain, then $\mathrm D$is UFD iff these conditions hold.

Published on 15 Apr 2026 - 14:11

score 84 · Answer 3 · 2026-04-16 05:03:15

84

Views

Dimension of a certain vector space

Published on 16 Apr 2026 - 5:03

score 278 · Answer 4 · 2026-04-12 11:12:55

278

Views

Height of finitely generated ideals in a catenary local ring

Published on 12 Apr 2026 - 11:12

score 101 · Answer 5 · 2026-04-14 16:11:40

101

Views

Integral domain (rings and fields)

Published on 14 Apr 2026 - 16:11

score 759 · Answer 6 · 2026-04-14 05:48:09

759

Views

Show that an integral domain $R$ is principal if and only if every submodule of a cyclic $R$-module is cyclic.

Published on 14 Apr 2026 - 5:48

score 79 · Answer 7 · 2026-04-14 11:29:47

79

Views

Show that if $R$ is principal, $N $ is pure and $Ann(x+N)= Rd$ then there exists $y \in M$ such that $x+N=y+N$ and $Ann(y)=Rd$

Published on 14 Apr 2026 - 11:29

score 209 · Answer 8 · 2026-04-15 11:13:04

209

Views

Facts about quotient rings - example

Published on 15 Apr 2026 - 11:13

score 4.1k · Answer 9 · 2026-04-11 15:10:06

4.1k

Views

Definition of irreducible element.

Published on 11 Apr 2026 - 15:10

score 2.5k · Answer 10 · 2026-04-15 03:24:56

2.5k

Views

the nonzero elements of Z3[i] form an abelian group of order 8 under multiplication. Is it isomorphic to Z8??

Published on 15 Apr 2026 - 3:24

score 130 · Answer 11 · 2026-04-13 18:29:18

130

Views

For some finitely many nonzero prime ideals, the contraction and extension of their product is zero

Published on 13 Apr 2026 - 18:29

score 608 · Answer 12 · 2026-04-13 05:59:46

608

Views

If the localization of a ring is a field, then the ring is an integral domain?

Published on 13 Apr 2026 - 5:59

score 763 · Answer 13 · 2026-04-14 18:43:04

763

Views

Exercise from Kaplansky's Commutative Rings and Eakin-Nagata Theorem

Published on 14 Apr 2026 - 18:43

score 190 · Answer 14 · 2026-04-15 04:17:00

190

Views

One dimensional noetherian domain

Published on 15 Apr 2026 - 4:17

score 82 · Answer 15 · 2026-05-11 06:19:26

82

Views

If an integral domain $R$ has a factorization basis, is it a UFD?

Published on 11 May 2026 - 6:19

List Question

$2$-dimensional Noetherian integrally closed domains are Cohen-Macaulay

Prove that if $\mathrm D$ is integral domain, then $\mathrm D$is UFD iff these conditions hold.

Dimension of a certain vector space

Height of finitely generated ideals in a catenary local ring

Integral domain (rings and fields)

Show that an integral domain $R$ is principal if and only if every submodule of a cyclic $R$-module is cyclic.

Show that if $R$ is principal, $N $ is pure and $Ann(x+N)= Rd$ then there exists $y \in M$ such that $x+N=y+N$ and $Ann(y)=Rd$

Facts about quotient rings - example

Definition of irreducible element.

the nonzero elements of Z3[i] form an abelian group of order 8 under multiplication. Is it isomorphic to Z8??

For some finitely many nonzero prime ideals, the contraction and extension of their product is zero

If the localization of a ring is a field, then the ring is an integral domain?

Exercise from Kaplansky's Commutative Rings and Eakin-Nagata Theorem

One dimensional noetherian domain

If an integral domain $R$ has a factorization basis, is it a UFD?

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