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Results tagged with completion
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user 14094
12
votes
Accepted
Can an intersection of ideals in a Noetherian ring be replaced by a countable intersection?
Yes it's true.
First, in a (commutative) noetherian ring $A$, every chain of ideals is well-ordered by reverse inclusion. The supremum of ordinal types of such chains is denoted $o(A)$.
A particula …
- 63.9k
7
votes
Accepted
Malcev completion of free groups
Here is a proof that the statement is, as you expected, false (for $n\ge 2$), in case the field $K$ is $\mathbf{R}$ or $\mathbf{C}$. Unfortunately it does not give anything explicit.
Let $B$ be its cl …
- 63.9k