Let Zps be the residue class ring of integers modulo ps, where p is a prime number and s is a positive integer. We study subspaces and Grassmann graphs for Zps n. A Grassmann graph for Zps n, denoted by Gd(n,m,ps) (Gd for short), has all m-subspaces of Zps n as its vertices, and two distinct vertices are adjacent if their intersection is of dimension >m−d, where m<n and 2≤d≤m+1. We give the clique number and geometric structures of maximum cliques of Gd, etc. By these results, we obtain the Erdős–Ko–Rado theorem for Zps n and some b...
