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.