Question

Kernel of $\mathbb{Z}_p \to \mathbb{Z}/p^{n}\mathbb{Z}$ equals to $p^n \mathbb{Z}_p$.

score 143 · Answer 1 · 2020-05-23 12:45:49

143

Views

Kernel of $\mathbb{Z}_p \to \mathbb{Z}/p^{n}\mathbb{Z}$ equals to $p^n \mathbb{Z}_p$.

Published on 23 May 2020 - 12:45

score 168 · Answer 2 · 2020-06-09 02:49:42

168

Views

If $I$ is contained in the Jacobson radical of a Noetherian ring $A$ then $A\to \widehat{A}$ is faithfully flat.

Published on 09 Jun 2020 - 2:49

score 127 · Answer 3 · 2020-06-11 15:06:05

127

Views

$R$ be a Noetherian semi local ring such that $R/N(R)$ is complete $\mathrm{Jac}(R)$-adically, then $R$ is complete $\mathrm{Jac}(R)$-adically.

Published on 11 Jun 2020 - 15:06

score 329 · Answer 4 · 2020-06-23 11:25:56

329

Views

Completion of a polynomial ring over a complete ring

Published on 23 Jun 2020 - 11:25

score 87 · Answer 5 · 2020-07-05 11:54:02

87

Views

Does the exist any ring embedding from $\mathbb{Z}_p$, the ring of $p$-adic integers to $\mathbb{R}$?

Published on 05 Jul 2020 - 11:54

score 153 · Answer 6 · 2020-07-05 14:50:27

153

Views

Defining p-adic numbers via a formal completion.

Published on 05 Jul 2020 - 14:50

score 114 · Answer 7 · 2026-02-23 06:37:58

114

Views

Defining p-adic numbers via formal competion: Question about continuity of multiplication

Published on 23 Feb 2026 - 6:37

score 117 · Answer 8 · 2020-07-13 16:12:51

117

Views

If $\widehat{M}$ is a free $\widehat{R}$-module, then $M$ is a free $R$-module, $R$ is a Zariski ring.

Published on 13 Jul 2020 - 16:12

score 129 · Answer 9 · 2020-07-14 00:40:29

129

Views

Relationship Between the Dimension of an $R / \mathfrak m$-Vector Space and Its Completion in the $\mathfrak m$-adic Topology

Published on 14 Jul 2020 - 0:40

score 204 · Answer 10 · 2020-07-15 10:06:47

204

Views

$\mathbb{Z}_p=\varprojlim \mathbb{Z}/p^{n}\mathbb{Z}$ is uncountable.

Published on 15 Jul 2020 - 10:06

score 204 · Answer 11 · 2020-07-23 08:19:53

204

Views

Complete DVR containing a field isomorphic to residue field

Published on 23 Jul 2020 - 8:19

score 597 · Answer 12 · 2017-02-07 17:24:48

597

Views

Completions, localizations and prime ideals.

Published on 07 Feb 2017 - 17:24

score 189 · Answer 13 · 2017-03-30 10:32:43

189

Views

How to describe formal functions around the node of an algebraic curve

Published on 30 Mar 2017 - 10:32

score 78 · Answer 14 · 2023-02-13 08:36:26

78

Views

If a Noetherian local ring contains a field, then so does its $\mathfrak m$-adic completion?

Published on 13 Feb 2023 - 8:36

score 20 · Answer 15 · 2023-06-07 16:59:16

20

Views

Is there any way to show that the algebraic tensor product $A[[h]] \otimes A[[h]] \subsetneq (A \otimes A) [[h]]\ $?

Published on 07 Jun 2023 - 16:59

List Question

Kernel of $\mathbb{Z}_p \to \mathbb{Z}/p^{n}\mathbb{Z}$ equals to $p^n \mathbb{Z}_p$.

If $I$ is contained in the Jacobson radical of a Noetherian ring $A$ then $A\to \widehat{A}$ is faithfully flat.

$R$ be a Noetherian semi local ring such that $R/N(R)$ is complete $\mathrm{Jac}(R)$-adically, then $R$ is complete $\mathrm{Jac}(R)$-adically.

Completion of a polynomial ring over a complete ring

Does the exist any ring embedding from $\mathbb{Z}_p$, the ring of $p$-adic integers to $\mathbb{R}$?

Defining p-adic numbers via a formal completion.

Defining p-adic numbers via formal competion: Question about continuity of multiplication

If $\widehat{M}$ is a free $\widehat{R}$-module, then $M$ is a free $R$-module, $R$ is a Zariski ring.

Relationship Between the Dimension of an $R / \mathfrak m$-Vector Space and Its Completion in the $\mathfrak m$-adic Topology

$\mathbb{Z}_p=\varprojlim \mathbb{Z}/p^{n}\mathbb{Z}$ is uncountable.

Complete DVR containing a field isomorphic to residue field

Completions, localizations and prime ideals.

How to describe formal functions around the node of an algebraic curve

If a Noetherian local ring contains a field, then so does its $\mathfrak m$-adic completion?

Is there any way to show that the algebraic tensor product $A[[h]] \otimes A[[h]] \subsetneq (A \otimes A) [[h]]\ $?

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