Question

If $x\in I$ is such that $\text{Supp}(0:_M x)\subseteq V(I)$ , then how to show that $x \notin \cup_{P\in \text{Ass}_R(M)\setminus V(I)} P $?

score 73 · Answer 1 · 2026-03-25 14:25:11

73

Views

If $x\in I$ is such that $\text{Supp}(0:_M x)\subseteq V(I)$ , then how to show that $x \notin \cup_{P\in \text{Ass}_R(M)\setminus V(I)} P $?

Published on 25 Mar 2026 - 14:25

score 148 · Answer 2 · 2021-09-17 19:58:12

148

Views

How to show that a set has a maximal element?

Published on 17 Sep 2021 - 19:58

score 82 · Answer 3 · 2026-03-29 13:24:23

82

Views

When an element of the total ring of fractions of a noetherian local ring $R$ is integral over $R$?

Published on 29 Mar 2026 - 13:24

score 331 · Answer 4 · 2021-09-21 11:31:24

331

Views

Exercise 11.4 in Atiyah & Macdonald's Commutative Algebra text

Published on 21 Sep 2021 - 11:31

score 53 · Answer 5 · 2021-09-23 18:50:40

53

Views

If $R\subseteq S$ is a split extension of Noetherian domains and $S$ is normal, then is $R$ normal?

Published on 23 Sep 2021 - 18:50

score 138 · Answer 6 · 2026-03-29 13:24:20

138

Views

On the natural map $\Phi_M: M\otimes_RM^\rightarrow\text{Hom}_R(M^,M^*),\ x\otimes y\mapsto \left\{f\mapsto f(x)y\right\} $

Published on 29 Mar 2026 - 13:24

score 564 · Answer 7 · 2021-10-02 00:27:44

564

Views

Does the ascending chain condition only apply to countable chains of ideals?

Published on 02 Oct 2021 - 0:27

score 34 · Answer 8 · 2026-03-29 03:12:23

34

Views

The algebraic implication of not being a Noetherian algebra

Published on 29 Mar 2026 - 3:12

score 99 · Answer 9 · 2026-03-27 20:21:10

99

Views

Show that If $A$ is Noetherian, then $A[[x_1,...,x_n]]$ is a faithfully flat $A$-algebra.

Published on 27 Mar 2026 - 20:21

score 105 · Answer 10 · 2026-03-29 18:32:52

105

Views

Let $A$ be an $1$-dimensional Noether integral domain. Let $I$ be an nonzero ideal of $A$.

Published on 29 Mar 2026 - 18:32

score 167 · Answer 11 · 2026-03-27 20:14:30

167

Views

Ideals in the ring of formal power series

Published on 27 Mar 2026 - 20:14

score 142 · Answer 12 · 2021-10-16 06:48:47

142

Views

Prove certain ring is noetherian.

Published on 16 Oct 2021 - 6:48

score 147 · Answer 13 · 2021-10-17 22:47:01

147

Views

Noetherian modules in exact sequence

Published on 17 Oct 2021 - 22:47

score 281 · Answer 14 · 2021-10-23 10:06:45

281

Views

Does $R[x]$ Noetherian imply $R[x,y]$ is Noetherian

Published on 23 Oct 2021 - 10:06

score 145 · Answer 15 · 2021-10-24 13:20:47

145

Views

Not Hilbert's basis theorem

Published on 24 Oct 2021 - 13:20

List Question

If $x\in I$ is such that $\text{Supp}(0:_M x)\subseteq V(I)$ , then how to show that $x \notin \cup_{P\in \text{Ass}_R(M)\setminus V(I)} P $?

How to show that a set has a maximal element?

When an element of the total ring of fractions of a noetherian local ring $R$ is integral over $R$?

Exercise 11.4 in Atiyah & Macdonald's Commutative Algebra text

If $R\subseteq S$ is a split extension of Noetherian domains and $S$ is normal, then is $R$ normal?

On the natural map $\Phi_M: M\otimes_RM^\rightarrow\text{Hom}_R(M^,M^*),\ x\otimes y\mapsto \left\{f\mapsto f(x)y\right\} $

Does the ascending chain condition only apply to countable chains of ideals?

The algebraic implication of not being a Noetherian algebra

Show that If $A$ is Noetherian, then $A[[x_1,...,x_n]]$ is a faithfully flat $A$-algebra.

Let $A$ be an $1$-dimensional Noether integral domain. Let $I$ be an nonzero ideal of $A$.

Ideals in the ring of formal power series

Prove certain ring is noetherian.

Noetherian modules in exact sequence

Does $R[x]$ Noetherian imply $R[x,y]$ is Noetherian

Not Hilbert's basis theorem

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