Show an isomorphism
I have to find this isomorphism:
Where and and is a well ordered increasing sequence of sub modules for .
I know that it is something about sending the residue class into the pair of residue classes
But how to argue that this is a homomorphism?
And what would the kernel be?
Any help would be nice, thanks.
Originally Posted by Carl
Pick any , then your map is just . You need to show that 1) the map is well-defined, by showing if (x1,y1), (x2,y2) differ by something in , then they map to the same thing, and 2) is a homomorphism (additive property and scalar multiplication property), which is easy to prove, and 3) 1-1 and onto, which is also not hard.