Prove that a non-zero principal weakly Artinian algebra possesses only one minimal ideal, and that ideal has a nonzero square, and in the associative case it is a simple algebra.

How to find all the homomorphisms between two residue class rings? Such as ，Zm to Zn? Er, I don't know how to express the problem exactly because i am just a beginner .Maybe a more specific question is: Find all the homomorphisms from Z15 to Z3(as ring)?