Cyclic codes over some special rings

In this paper we will study cyclic codes over some special rings: F_{q}[u]/(u^{i}), F_{q}[u_1,…u_{i}]/(u_1^2,u_2^2,…,u_{i}^2, u_1 u_2 - u_2 u_1,…,u_{i}u_{j} - u_{j}u_{i},…), F_{q}[u,v]/(u^{i},v^{j},uv-vu), q=p^{r}, where p is a prime number, r\in N-{0} and F_{q} is a field with q elements.