On the multiplicative monoid of n×nn×n matrices over ZpmZpm

For any positive integers m,nm,n and a prime number p  , we introduce the concept of invariant factors for matrices over ZpmZpm first, then investigate Green's relations, Green's relation equivalence classes, Schützenberger groups of DD-classes, group HH-classes and regular principal factors of the matrix multiplicative monoid Mn(Zpm)Mn(Zpm). As corollaries, we characterize a matrix which has a group inverse in Mn(Zpm)Mn(Zpm).