Depth of modular invariant rings

It is well-known that the ring of invariants associated to a nea-modular re presentation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation. For modular representations the rin g of invariants usually fails to be Cohen-Macaulay and computing the depth is often very difficult. In this paper(1) we obtain a simple formula for th e depth of the ring of invariants for a family of modular representations. This family includes all modular representations of cyclic groups. Tn parti cular, we obtain an elementary proof of the celebrated theorem of Ellingsru d and Skjelbred [6].