Question

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

score 656 · Answer 1 · 2026-03-25 07:42:57

656

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

Published on 25 Mar 2026 - 7:42

score 199 · Answer 2 · 2014-06-10 13:23:41

199

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

Published on 10 Jun 2014 - 13:23

score 81 · Answer 3 · 2014-06-13 19:47:03

81

Views

Dimension of a certain vector space

Published on 13 Jun 2014 - 19:47

score 275 · Answer 4 · 2014-06-15 12:43:38

275

Views

Height of finitely generated ideals in a catenary local ring

Published on 15 Jun 2014 - 12:43

score 98 · Answer 5 · 2014-06-18 09:15:52

98

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Integral domain (rings and fields)

Published on 18 Jun 2014 - 9:15

score 756 · Answer 6 · 2014-06-20 13:49:29

756

Views

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

Published on 20 Jun 2014 - 13:49

score 76 · Answer 7 · 2014-06-25 12:45:42

76

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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 25 Jun 2014 - 12:45

score 206 · Answer 8 · 2014-06-25 13:53:27

206

Views

Facts about quotient rings - example

Published on 25 Jun 2014 - 13:53

score 4.1k · Answer 9 · 2014-06-26 06:43:31

4.1k

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Definition of irreducible element.

Published on 26 Jun 2014 - 6:43

score 2.5k · Answer 10 · 2014-07-01 05:31:50

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 01 Jul 2014 - 5:31

score 127 · Answer 11 · 2014-07-01 10:23:19

127

Views

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

Published on 01 Jul 2014 - 10:23

score 605 · Answer 12 · 2014-07-01 13:01:21

605

Views

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

Published on 01 Jul 2014 - 13:01

score 760 · Answer 13 · 2014-07-02 04:55:53

760

Views

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

Published on 02 Jul 2014 - 4:55

score 187 · Answer 14 · 2014-07-03 06:44:06

187

Views

One dimensional noetherian domain

Published on 03 Jul 2014 - 6:44

score 78 · Answer 15 · 2014-07-07 13:15:33

78

Views

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

Published on 07 Jul 2014 - 13:15

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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