I'm having problems showing that Q is indecomposable as a module over Z (abelian group).
My thoughts: if Q = A+B (direct sum of submodules A,B) then B = Q/A so we must have both A and Q/A to not be finitely generated. But i'm guessing Q has subgroups which aren't finitely generated so i don't think this helps at all.
Can anyone give me some hints?
My thoughts: if Q = A+B (direct sum of submodules A,B) then B = Q/A so we must have both A and Q/A to not be finitely generated. But i'm guessing Q has subgroups which aren't finitely generated so i don't think this helps at all.
Can anyone give me some hints?