For modules we can say "External direct sum is associative and commutative up to isomorphism." If we are using internal direct sum I think we can say it is associative and commutative (They are equal not only isomorphic). Am I right? I tried to prove and didn't see any problem. I mean I can say;
Let A,B,C are submodules of M then $ M=A \oplus B \Rightarrow M=B \oplus A $
and
$ M=(A\oplus B)\oplus C \Rightarrow M=A \oplus(B\oplus C) $
Right?