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Results tagged with modules
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user 43107
For questions on modules over rings.
5
votes
Divisible torsion $\mathbb{Z}$-modules
Since $\mathbf{Q}/\mathbf{Z} = \varinjlim (1/n) \mathbf{Z}/\mathbf{Z}$ and $V = \varinjlim V[n]$ (as $V$ is torsion), it suffices to show that for $n > 0$ the natural map ${\rm{Hom}}(\mathbf{Q}/\mathb …
- 1,623
1
vote
Simultaneous decomposition of modules over Dedekind domains
There will then be nothing to do if $r=1$, and if $r > 1$ we use rank-induction to describe these modules compatibly as direct sums of invertible modules in such a way that for the ambient $D$-module all … Continuing via induction on $r > 1$, we get compatible decompositions of $M_2$ and $M_1$ as direct sums of invertible $D$-modules in such a way that all but one of the invertible $D$-modules using for …