Cyclic codes and λ1+λ2u+λ3v+λ4uv-constacyclic codes over Fp+uFp+vFp+uvFp

Let R=Fp+uFp+vFp+uvFp, where p is a prime and u2=u,v2=v,uv=vu. It is a semi-local ring, not a chain ring. In this paper, some properties of linear codes over the ring R are studied. The generator of cyclic codes and λ1+λ2u+λ3v+λ4uv-constacyclic codes over R are given. A necessary and sufficient condition for self-dual cyclic codes over R is given.