Abstract
An associative Artinian ring with an identity is a chain ring if its lattice of left (right) ideals forms a unique chain. In this article, we first prove that for every chain ring, there exists a certain finite commutative chain subring which characterizes it. Using this fact, we classify chain rings with invariants p, n, r, k, k', m up to isomorphism by finite commutative chain rings (k' = 1). Thus the classification of chain rings is reduced to that of finite commutative chain rings.