Assignment:
Let R be a subring of a ring S and let
0 -> M -> N -> P -> 0
be a short exact sequence of S-modules. Prove or disprove the following statements:
(i) If the sequence is split over S, then it is split over R.
(ii) If the sequence is split over R, then it is split over S.
Provide complete and step by step solution for the question and show calculations and use formulas.