I am trying to understand the completion $\hat R$ of a commutative unitary ring $R$ w.r.t. an ideal $J$. Please let me first recall, what I think is true (since if there is a misunderstanding already, I would be very glad for pointing it out).
The ideal $J$ defines the $J$-adic topology on $R$ b...
I'm reading chapter 10 of A-M in Completions, and I'm trying to understand how coherent sequences give rise to Cauchy sequences. This seems to be pretty clear, according to the text, but it eludes me.
Specifically, it says the following:
Given any coherent sequence $(\zeta_n)$, (in the sens...
Maybe someone more knowledgeable in commutative-algebra could say whether it is a useful tag (and perhaps suggest a tag-excerpt/tag-wiki.)
I have also pinged the user who probably created the tag:
@Doldrums I see that you created the tag (formal-completions) in your edit. (At least this is the oldest occurrence of that tag that I found.) When creating a tag, it is useful to also add tag-wiki (or at least tag-excerpt) explaining briefly what the tag is supposed to be used for. Feel free to drop me a line in chat if some more details are needed. — Martin Sleziak26 secs ago
@Doldrums If you come to this chatroom and will read this: You should not be afraid if you see that you do not have reputation to edit tag-wikis. You still can suggest edits on a tag-wiki, then it has to be approved by other users.
I'm reading chapter 10 of A-M in Completions, and I'm trying to understand how coherent sequences give rise to Cauchy sequences. This seems to be pretty clear, according to the text, but it eludes me.
Specifically, it says the following:
Given any coherent sequence $(\zeta_n)$, (in the sens...
