List questions from noetherian

Published on 25 Jan 2014 - 11:50

151

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Why is the tight closure tightly closed?

Published on 25 Mar 2026 - 19:59

319

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$f$ is contained in no codimension $0,1$ primes $\implies f$ is invertible. Why do we need codim 1 primes as well?

Published on 06 Feb 2014 - 12:54

3.1k

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Nontrivial ideal of a Noetherian domain contains a finite product of nonzero prime ideals

Published on 07 Feb 2014 - 1:05

2.4k

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Is the integral closure of an integrally closed Noetherian domain in a finite extension field Noetherian?

Published on 25 Mar 2026 - 6:06

1.1k

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Coherent sheaves of finite length

Published on 08 Feb 2014 - 3:21

556

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A proof of the Noether Normalization Lemma

Published on 08 Feb 2014 - 23:24

968

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Dimension of graded module

Published on 26 Mar 2026 - 7:57

395

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Show that $R$ is a Noetherian Ring

Published on 10 Feb 2014 - 18:14

41

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existence of a factorization morphism related to extension fields

Published on 10 Feb 2014 - 18:53

159

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Define, $p^{-1} = \{x \in K: xp \subset D\}$. Then show that there exists a non zero $c \in D$ such that $cp^{-1} \subset D$.

Published on 11 Feb 2014 - 4:54

804

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If $k\subset R\subset k[x]$, then $R$ is Noetherian?

Published on 12 Feb 2014 - 5:16

627

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Example of non-noetherian algebras which are tensor products of noetherian algebras

Published on 20 Feb 2014 - 22:42

623

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Infinitesimal thickening of a smooth closed subscheme

Published on 05 Mar 2014 - 12:39

275

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Associated primes and finite base change

Published on 07 Mar 2014 - 17:12

List Question

Subrings of polynomial rings over the complex plane

Why is the tight closure tightly closed?

$f$ is contained in no codimension $0,1$ primes $\implies f$ is invertible. Why do we need codim 1 primes as well?

Nontrivial ideal of a Noetherian domain contains a finite product of nonzero prime ideals

Is the integral closure of an integrally closed Noetherian domain in a finite extension field Noetherian?

Coherent sheaves of finite length

A proof of the Noether Normalization Lemma

Dimension of graded module

Show that $R$ is a Noetherian Ring

existence of a factorization morphism related to extension fields

Define, $p^{-1} = \{x \in K: xp \subset D\}$. Then show that there exists a non zero $c \in D$ such that $cp^{-1} \subset D$.

If $k\subset R\subset k[x]$, then $R$ is Noetherian?

Example of non-noetherian algebras which are tensor products of noetherian algebras

Infinitesimal thickening of a smooth closed subscheme

Associated primes and finite base change

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