8. Prove the following generalization of the well-known Chinese remainder theorem: Let R be a ring with unit element and let A1,A2,….An(n⩾2) be pairwise relative prime ideals of R. Then, for arbitrary elements c1,c2,…,cn of R, there exists an element x∈R such that x−ck∈Ak(k=1,2,…,n). (A. 17) Ring Theorycollege contests