If you want to be real nitpicky you shouldn't be using '+' for non-commutative operations either. Ideally you'd also have some kind of distributive law, but if

If you want to be real nitpicky you shouldn't be using '+' for non-commutative operations either. Ideally you'd also have some kind of distributive law, but if needs be any commutative operation will naturally result in a module over the integers, which I suppose works well enough.