Cyclic codes over the ring $\mathbb{F}_p[u, v, w]/\langle u^2, v^2, w^2, uv-vu, vw-wv, uw-wu \rangle$

In this paper, we investigate cyclic codes over the ring Fp[u, v, w]〈u , v, w, uv− vu, vw − wv, uw − wu〉, where p is a prime number. Which is a part of family of Frobenius rings. We find a unique set of generators for these codes and characterize the free cyclic codes. We also study the rank and the Hamming distance of these codes. We also constructs some good p−ary codes as the Gray images of these cyclic codes.