  Let R be an associative ring with identity. We study an elementary
generalization of the classical Zariski topology, applied to the set of
isomorphism classes of simple left R-modules (or, more generally, simple
objects in a complete abelian category). Under this topology the points are
closed, and when R is left noetherian the corresponding topological space is
noetherian. If R is commutative (or PI, or FBN) the topology is equivalent to
the Zariski topology, and when R is the first Weyl algebra (in characteristic
zero) we obtain a one-dimensional irreducible noetherian topological space.
Comparisons with topologies induced from those on A. L. Rosenberg's spectra are
briefly noted.
