Timeline for When is the profinite completion of a Noetherian group ring also Noetherian?

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Aug 9, 2021 at 3:10	comment	added	stupid_question_bot		@MartinBrandenburg The completed ring for $G = \mathbb{Z}$ is described here. It is the product of $\mathbb{Z}_q[[t]]$, where each $q$ is a prime power and the corresponding direct factor appears multiple times (number of times is equal to the number of Frobenius orbits on $\mathbb{F}_q^\times$). It certainly does not satisfy ACC, but this doesn't necessarily mean that there exists an infinitely generated closed ideal, since the union of the ascending chain may not be closed.
Aug 8, 2021 at 22:58	comment	added	Martin Brandenburg		How can we describe that completed ring for $G = \mathbb{Z}$ more concretely?
Aug 8, 2021 at 3:44	history	edited	stupid_question_bot	CC BY-SA 4.0	added 61 characters in body
Aug 7, 2021 at 17:35	history	edited	stupid_question_bot	CC BY-SA 4.0	added 158 characters in body
Aug 7, 2021 at 9:07	history	edited	YCor		edited tags; edited tags
Aug 7, 2021 at 9:07	comment	added	YCor		The only groups $G$ for which $Z[G]$ is known to be noetherian are virtually polycyclic groups. (Conversely, if $Z[G]$ is noetherian, it is known that $G$ is noetherian and amenable. See this MO answer)
Aug 7, 2021 at 6:44	history	asked	stupid_question_bot	CC BY-SA 4.0