Timeline for Is the completion of an infinitely generated module, again infinitely generated

8 events

when toggle format	what		by	license	comment
Nov 2, 2019 at 11:27	comment	added	Angelo		Completing a module that is not finitely generated is often very bad for its health. That's why derived completion (a gentler kind of completion) was invented (just do a google search).
Nov 2, 2019 at 10:42	comment	added	abx		Your edited condition does not help: take the fraction field of $A/\mathfrak{p}$, where $\mathfrak{p}$ is any prime ideal strictly contained in $\mathfrak{m}$.
Nov 2, 2019 at 10:39	comment	added	Wojowu		Consider $\mathbb Z_p$ as a module over $\mathbb Z_{(p)}$. It is infinitely (even uncountably) generated for cardinality reason, but taking the completions we get $\mathbb Z_p$ over $\mathbb Z_p$.
Nov 2, 2019 at 10:08	comment	added	Ron		@Angelo Thank you. I have edited the question slightly with an additional condition on the support.
Nov 2, 2019 at 10:05	history	edited	Ron	CC BY-SA 4.0	added 95 characters in body
Nov 2, 2019 at 9:58	history	edited	Ron	CC BY-SA 4.0	added 122 characters in body
Nov 2, 2019 at 9:45	comment	added	Angelo		The $\frak m$-adic completion could even be 0 (for example, when $A$ is domain and $M$ is its fraction field).
Nov 2, 2019 at 9:41	history	asked	Ron	CC BY-SA 4.0