Abstract: Let R=Z/p^kZ be the ring of integers modulo p^k where p is a prime and k>1.Denote by n(r,m×n)tile number of m by n matrices with real rank r over R.In tile present paper. we compute n(r.m×n) and the number of the orbits of Mm,n(R) under GLm(R)×GLn(R).where Mm.n(R) is the set of all m by n matrices over R.

Key words: Anzahl theorem, orbits, ring Z/p^kZ