Representing Diagrams and M-Ideals in L_(1)-Predual Spaces

We continue the study of diagrammatic representations of separable L1-predual spaces and show that given an M-ideal M in a C(K)-space, there exists a diagram of C(K) such that M is given by a directed sub-diagram. Similar results are true also for the spaces C0(T), c and c0. This allows one to find a representing matrix of an M-ideal in these spaces. We also obtain some partial results for hyperplanes that are M-ideals in separable L1-predual spaces.