Has property that,
Well that is simple to show,
Any element of can be expressed as,
And every (for it is closed since it is a ring).
Now the other way around is also true for any element of can be expressed as,
But since is a commutative ring,
That part is finished.
The question remains to show that this generating set is an additive subgroup of the ring. I am not going to show that (in fact it is simple to) but you show be familar from group theory that these generating sets always forms a subgroup (if one element only then it is a cyclic subgroup).