  In this article we extend the notion of expansivity from topological dynamics
to automorphisms of commutative rings with identity. We show that a ring admits
a 0-expansive automorphism if and only if it is a finite product of local
rings. Generalizing a well known result of compact metric spaces, we prove that
if a ring admits a positively expansive automorphism then it admits finitely
many maximal ideals. We prove its converse for principal ideal domains. We also
consider the topological expansivity induced, in the spectrum of the ring with
the Zariski topology, by an automorphism and some consequences are derived.
