Let R_e =F_{p^m}[u]/⟨u^e⟩, where p is a prime number, e is a positive integer and u^e = 0. In this paper, we first characterize the structure of cyclic codes of length p^s over R_e. These codes will be classified into 2^e distinct types. Among other results, in the case that e = 4, the torsion codes of cyclic codes of length p^s over R_4 are obtained. Also, we present some examples of cyclic codes of length p^s over R_e.
