Question

Dimension of $(A[[X]])_\mathfrak{m} \geq k+1$, regular ring, chain of prime ideals

score 39 · Answer 1 · 2026-03-25 06:06:22

39

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Dimension of $(A[[X]])_\mathfrak{m} \geq k+1$, regular ring, chain of prime ideals

Published on 25 Mar 2026 - 6:06

score 101 · Answer 2 · 2023-02-23 23:21:14

101

Views

Eventual vanishing of $\operatorname{Ext}^i_R(M,N)$ Vs. eventual vanishing of $\operatorname{Ext}^i_R(M,R)$, where $N$ has projective dimension $2$

Published on 23 Feb 2023 - 23:21

score 87 · Answer 3 · 2023-02-24 21:27:58

87

Views

Ideals of zero intersection are in powers of the maximal ideal

Published on 24 Feb 2023 - 21:27

score 138 · Answer 4 · 2023-02-25 01:51:01

138

Views

Derived tensor product of finitely generated module of finite projective dimension and bounded above chain complex of finitely generated free modules

Published on 25 Feb 2023 - 1:51

score 86 · Answer 5 · 2023-03-01 09:36:31

86

Views

The set of non-zero-divisors is dense in the $\mathfrak m$-adic topology for a Noetherian local ring of positive depth

Published on 01 Mar 2023 - 9:36

score 176 · Answer 6 · 2026-03-25 08:12:45

176

Views

Residue field of DVR

Published on 25 Mar 2026 - 8:12

score 118 · Answer 7 · 2023-03-17 18:28:55

118

Views

Freeness of $I/I^2$ implies that of $\dfrac{I}{I^2+xR}$ over $R/I$?

Published on 17 Mar 2023 - 18:28

score 52 · Answer 8 · 2026-02-23 03:58:10

52

Views

When is the intersection of every non-zero ideal with socle again non-zero?

Published on 23 Feb 2026 - 3:58

score 113 · Answer 9 · 2026-03-25 14:07:38

113

Views

Ideal of definition of local ring

Published on 25 Mar 2026 - 14:07

score 37 · Answer 10 · 2023-03-24 06:52:23

37

Views

left bounded chain complex $Z$ such that $Z \otimes_R^{\mathbf L} (R_P/PR_P)$ is uniformly right bounded as $P$ varies over prime ideals of $R$

Published on 24 Mar 2023 - 6:52

score 65 · Answer 11 · 2026-03-25 11:16:28

65

Views

On local rings $(R, \mathfrak m)$ such that $\text{Spec}(R)$ is disjoint union of $\text{Ass}(R)$ and $ \{\mathfrak m \}$

Published on 25 Mar 2026 - 11:16

score 73 · Answer 12 · 2023-04-03 04:32:20

73

Views

non-free module of finite projective dimension and locally free on punctured spectrum on a local non-Cohen-macaulay ring

Published on 03 Apr 2023 - 4:32

score 19 · Answer 13 · 2023-04-17 02:27:22

19

Views

Prove that if $P ∈ C(\overline{K})$ is a pole of $f ∈ K(C)$, then $v_P(f) < 0$ and $P$ is a zero of $1/f$.

Published on 17 Apr 2023 - 2:27

score 77 · Answer 14 · 2026-03-25 06:05:49

77

Views

Examples of Gorenstein local unique factorization domain of dimension $2$ and embedding dimension $4$

Published on 25 Mar 2026 - 6:05

score 32 · Answer 15 · 2023-04-20 11:30:45

32

Views

On finding certain minimal generating set of the maximal ideal in a local ring of positive depth

Published on 20 Apr 2023 - 11:30

List Question

Dimension of $(A[[X]])_\mathfrak{m} \geq k+1$, regular ring, chain of prime ideals

Eventual vanishing of $\operatorname{Ext}^i_R(M,N)$ Vs. eventual vanishing of $\operatorname{Ext}^i_R(M,R)$, where $N$ has projective dimension $2$

Ideals of zero intersection are in powers of the maximal ideal

Derived tensor product of finitely generated module of finite projective dimension and bounded above chain complex of finitely generated free modules

The set of non-zero-divisors is dense in the $\mathfrak m$-adic topology for a Noetherian local ring of positive depth

Residue field of DVR

Freeness of $I/I^2$ implies that of $\dfrac{I}{I^2+xR}$ over $R/I$?

When is the intersection of every non-zero ideal with socle again non-zero?

Ideal of definition of local ring

left bounded chain complex $Z$ such that $Z \otimes_R^{\mathbf L} (R_P/PR_P)$ is uniformly right bounded as $P$ varies over prime ideals of $R$

On local rings $(R, \mathfrak m)$ such that $\text{Spec}(R)$ is disjoint union of $\text{Ass}(R)$ and $ \{\mathfrak m \}$

non-free module of finite projective dimension and locally free on punctured spectrum on a local non-Cohen-macaulay ring

Prove that if $P ∈ C(\overline{K})$ is a pole of $f ∈ K(C)$, then $v_P(f) < 0$ and $P$ is a zero of $1/f$.

Examples of Gorenstein local unique factorization domain of dimension $2$ and embedding dimension $4$

On finding certain minimal generating set of the maximal ideal in a local ring of positive depth

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