Cyclic Codes over F_p + uF_p + vF_p + uvF_p

In this paper,cyclic codes over the ring R=F_p+uF_p+vF_p+uvF_p are discussed,where the ring R is not a finite chain ring.By studying the polynomial ring R_n=(F_p +uF_p +vF_p +uvF_p)[x]/(x~n-1) and using the corresponding relationship between the cyclic codes over the ring R and the ideals in the ringR_n,cyclic codes over the ring R are characterized.Finally,a Gray-map is obtained and the images of cyclic codes over the ring R are characterized.