Question

Do we have $\bigcap_{1\leq i\leq r}(\mathfrak{m}^n+\mathfrak{p}_i)=\mathfrak{m}^n$ in a local ring, where $\mathfrak{p_i}$ are the minimal primes?

score 51 · Answer 1 · 2023-09-19 09:16:34

51

Views

Do we have $\bigcap_{1\leq i\leq r}(\mathfrak{m}^n+\mathfrak{p}_i)=\mathfrak{m}^n$ in a local ring, where $\mathfrak{p_i}$ are the minimal primes?

Published on 19 Sep 2023 - 9:16

score 107 · Answer 2 · 2023-09-25 11:06:16

107

Views

Is the ring of formal power series a localization of some non local ring at prime ideals?

Published on 25 Sep 2023 - 11:06

score 71 · Answer 3 · 2023-10-10 17:02:12

71

Views

Betti numbers of associated graded ring

Published on 10 Oct 2023 - 17:02

score 44 · Answer 4 · 2023-10-16 12:57:22

44

Views

Equivalent definitions of a local algebra

Published on 16 Oct 2023 - 12:57

score 59 · Answer 5 · 2023-10-20 23:58:02

59

Views

On pushforward functor and freeness of modules

Published on 20 Oct 2023 - 23:58

score 97 · Answer 6 · 2023-10-22 07:22:48

97

Views

How can I show that if $x$ is a nonunit then $1-x$ is a unit?

Published on 22 Oct 2023 - 7:22

score 81 · Answer 7 · 2026-03-25 14:29:21

81

Views

Serre conditions and local isomorphisms

Published on 25 Mar 2026 - 14:29

score 80 · Answer 8 · 2023-11-06 05:37:51

80

Views

Module over a commutative local ring has nonzero homomorphism

Published on 06 Nov 2023 - 5:37

score 49 · Answer 9 · 2023-11-06 16:34:18

49

Views

Is a flat extension of DVRs always finite?

Published on 06 Nov 2023 - 16:34

score 50 · Answer 10 · 2023-11-19 11:23:11

50

Views

How to express elements of a DVR as power series of the uniformizer?

Published on 19 Nov 2023 - 11:23

score 83 · Answer 11 · 2023-11-22 16:27:32

83

Views

Proving two modules are free based on their direct sum

Published on 22 Nov 2023 - 16:27

score 213 · Answer 12 · 2023-12-03 03:33:22

213

Views

Does this local ring have a name?

Published on 03 Dec 2023 - 3:33

score 60 · Answer 13 · 2023-12-04 19:45:08

60

Views

If $f:\operatorname{Spec} R \to X$ is a map with $R$ local and with closed point landing in an open $U\subset X$, then $im(f)\subset U$ too.

Published on 04 Dec 2023 - 19:45

score 63 · Answer 14 · 2023-12-05 20:20:56

63

Views

If $R$ is a local ring, the morphism of schemes $f: \operatorname{Spec} R \to X$ is determined by the image of the closed point?

Published on 05 Dec 2023 - 20:20

score 83 · Answer 15 · 2023-12-07 11:44:59

83

Views

On idempotents and local property of $\Lambda \otimes_R R_{\mathfrak p}$ where $\Lambda$ is module finite algebra over commutative local ring $R$

Published on 07 Dec 2023 - 11:44

List Question

Do we have $\bigcap_{1\leq i\leq r}(\mathfrak{m}^n+\mathfrak{p}_i)=\mathfrak{m}^n$ in a local ring, where $\mathfrak{p_i}$ are the minimal primes?

Is the ring of formal power series a localization of some non local ring at prime ideals?

Betti numbers of associated graded ring

Equivalent definitions of a local algebra

On pushforward functor and freeness of modules

How can I show that if $x$ is a nonunit then $1-x$ is a unit?

Serre conditions and local isomorphisms

Module over a commutative local ring has nonzero homomorphism

Is a flat extension of DVRs always finite?

How to express elements of a DVR as power series of the uniformizer?

Proving two modules are free based on their direct sum

Does this local ring have a name?

If $f:\operatorname{Spec} R \to X$ is a map with $R$ local and with closed point landing in an open $U\subset X$, then $im(f)\subset U$ too.

If $R$ is a local ring, the morphism of schemes $f: \operatorname{Spec} R \to X$ is determined by the image of the closed point?

On idempotents and local property of $\Lambda \otimes_R R_{\mathfrak p}$ where $\Lambda$ is module finite algebra over commutative local ring $R$

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