Question

Extension of continuous map on group ring to a map on the complete group algebra

score 78 · Answer 1 · 2026-03-17 10:00:19

78

Views

Extension of continuous map on group ring to a map on the complete group algebra

Published on 17 Mar 2026 - 10:00

score 279 · Answer 2 · 2026-03-17 08:47:48

279

Views

$R$ be Noetherian ring. Let $I \subseteq J$ be proper ideals of $R$. If $R$ is $J$-adically complete, then is $R$ complete $I$-adically?

Published on 17 Mar 2026 - 8:47

score 272 · Answer 3 · 2026-03-17 13:50:06

272

Views

$I$ be a finitely generated ideal of $R$ such that $R/I$ is a Noetherian and $R$ is $I$-adically complete. Then $R$ is Noetherian

Published on 17 Mar 2026 - 13:50

score 80 · Answer 4 · 2026-03-17 14:31:30

80

Views

$R$ is Noetherian semilocal. $J:=\operatorname{Jac}(R)$. If $R/\operatorname{nil}(R)$ is $J$-adically complete, then $R$ is $J$-adically complete

Published on 17 Mar 2026 - 14:31

score 56 · Answer 5 · 2026-03-17 13:10:13

56

Views

$\mathbb{Z}_p[\mathbb{Z}/p^{n}\mathbb{Z}]\cong \mathbb{Z}_p[T]/\left((T+1)^{p^n}-1\right)$ as topological rings?

Published on 17 Mar 2026 - 13:10

score 121 · Answer 6 · 2026-03-17 15:32:24

121

Views

Is $\mathbb R$ with usual euclidean topology, homeomorphic with some topological field of positive characteristic?

Published on 17 Mar 2026 - 15:32

score 111 · Answer 7 · 2026-03-17 10:59:33

111

Views

Could we define injective modules or projective modules for topological modules?

Published on 17 Mar 2026 - 10:59

score 137 · Answer 8 · 2026-03-17 07:43:56

137

Views

Making the subgroup of units of a topological ring a topological group

Published on 17 Mar 2026 - 7:43

score 178 · Answer 9 · 2026-03-15 04:52:09

178

Views

What's in a Noetherian $\mathbb{A}$-Module Ephemeralization?

Published on 15 Mar 2026 - 4:52

score 119 · Answer 10 · 2026-03-17 17:56:13

119

Views

Is the ring $R$ a topological ring with respect to the following topology?

Published on 17 Mar 2026 - 17:56

score 22 · Answer 11 · 2026-03-17 10:25:35

22

Views

How can we add small numbers to an element of a topological ring to make neighborhoods?

Published on 17 Mar 2026 - 10:25

score 619 · Answer 12 · 2026-03-20 08:17:13

619

Views

Is closure of an ideal also an ideal?

Published on 20 Mar 2026 - 8:17

score 341 · Answer 13 · 2026-03-19 22:53:35

341

Views

Topological vector spaces over field with discrete topology

Published on 19 Mar 2026 - 22:53

score 360 · Answer 14 · 2026-03-20 07:16:12

360

Views

Group Rings of Topological Groups and Fields

Published on 20 Mar 2026 - 7:16

score 100 · Answer 15 · 2026-03-20 17:41:35

100

Views

Are (co)limits of topological rings in $\mathsf{Ring}$ with continuous legs always a (co)limit in $\mathsf{Top}$ for a suitable topology?

Published on 20 Mar 2026 - 17:41

List Question

Extension of continuous map on group ring to a map on the complete group algebra

$R$ be Noetherian ring. Let $I \subseteq J$ be proper ideals of $R$. If $R$ is $J$-adically complete, then is $R$ complete $I$-adically?

$I$ be a finitely generated ideal of $R$ such that $R/I$ is a Noetherian and $R$ is $I$-adically complete. Then $R$ is Noetherian

$R$ is Noetherian semilocal. $J:=\operatorname{Jac}(R)$. If $R/\operatorname{nil}(R)$ is $J$-adically complete, then $R$ is $J$-adically complete

$\mathbb{Z}_p[\mathbb{Z}/p^{n}\mathbb{Z}]\cong \mathbb{Z}_p[T]/\left((T+1)^{p^n}-1\right)$ as topological rings?

Is $\mathbb R$ with usual euclidean topology, homeomorphic with some topological field of positive characteristic?

Could we define injective modules or projective modules for topological modules?

Making the subgroup of units of a topological ring a topological group

What's in a Noetherian $\mathbb{A}$-Module Ephemeralization?

Is the ring $R$ a topological ring with respect to the following topology?

How can we add small numbers to an element of a topological ring to make neighborhoods?

Is closure of an ideal also an ideal?

Topological vector spaces over field with discrete topology

Group Rings of Topological Groups and Fields

Are (co)limits of topological rings in $\mathsf{Ring}$ with continuous legs always a (co)limit in $\mathsf{Top}$ for a suitable topology?

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