Noetherianity of the Space of Irreducible Representations
نویسندگان
چکیده
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 Rmodules (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 onedimensional irreducible noetherian topological space. Comparisons with topologies induced from those on A. L. Rosenberg’s spectra are briefly noted.
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