This is a standard problem I've seen, but I am new to tensors. If I could see the proof I think it would help me greatly to compute tensors in general.
The problem statement here is from Hungerford GTM section IV.5.2
Show where c is gcd(m,n).
(everything is regarded as an add. abelian group-- the tensor is over Z)
A lead question is to show , which I think I managed with the map f sending showing the kernel was 0 and was surjective. For what it's worth, as a bijection this implies elements of are required to have the form simply -- whether or not this will help with the problem stated above has not been something I can reconcile on my own.
Any insights would be appreciated greatly.