.I have to find this isomorphism:
Where and and is a well ordered increasing sequence of sub modules for .
What do you mean by "well-ordered increasing seq. of submod. of..."?? That is indexed by a countable index set and thus , or
only that for any two indexes , either ?
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.