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Results tagged with modules
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user 62635
For questions on modules over rings.
10
votes
2
answers
343
views
An example of a non-geometric $C^\infty(M)$-module
.$ Hence we have to look for non-geometric modules in a different way. …
- 1,615
2
votes
1
answer
197
views
Why is $C^\infty(M)$-module homomorphism $P\mapsto\Gamma(P)$ surjective?
Show that $P$ is geometric if and only if the two modules $P$ and $\Gamma(P)$ are isomorphic.
It is clear that there is an injective map from $P$ to $\Gamma(P)$ iff $P$ is geometric. …
- 1,615
2
votes
Accepted
Why is $C^\infty(M)$-module homomorphism $P\mapsto\Gamma(P)$ surjective?
The exercise is fine. I misread the definition of $\Gamma(P).$ Jet Nestruev defines $\Gamma(P)$ as an image $\phi(P).$ Hence surjectivity follows obviously from the definition of $\Gamma(P)$.
- 1,615