Let φ be a ring homomorphism from a ring R to a ring S. Let A be a subring of R and B an ideal of S.
Complete the following statements.
1. For any r ∈ R and any positive integer n,
φ(nr) = ______ and φ(rn) = ______.
2. φ(A) is ______ of S.
3. If A is an ideal and is onto S, then φ(A) is ______ of S.
4. φ-1(B) is ______ of R.
5. If R is commutative, then ________ is commutative.