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Results tagged with modules
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user 4794
For questions on modules over rings.
4
votes
$R$ a DVR with fraction field $K.$ What are the $R$-submodules of $K^n?$
Fix a prime $p$ and let $x$ be a $p$-adic integer that is not a rational number.
Now let $M$ be the group of pairs of rational numbers $(r,s)$ so that $rx-s$ is
a $p$-adic integer.
Then $M$ maps ont …
- 3,504
11
votes
Non-finite version of Nakayama's lemma?
Let $N$ be the $A$-module generated by $S$. Now $M$ is contained in $N+\mathfrak{m}M$,
which is contained in $N+\mathfrak{m}(N+\mathfrak{m}M)$, hence in $N+\mathfrak{m}^2M$.
Repeat.
- 3,504