The Closed-Point Zariski Topology for Irreducible Representations

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dc.creatorGoodearl, K. R.
dc.creatorLetzter, E. S.
dc.date2005-07-27
dc.date.accessioned2026-07-07T05:22:02Z
dc.date.available2026-07-07T05:22:02Z
dc.descriptionIn previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings. In this paper, a concise and elementary description of this refined Zariski topology is presented, under certain hypotheses, for the space of simple left modules over a ring R. Namely, if R is left noetherian (or satisfies the ascending chain condition for semiprimitive ideals), and if R is either a countable dimensional algebra (over a field) or a ring whose (Gabriel-Rentschler) Krull dimension is a countable ordinal, then each closed set of the refined Zariski topology is the union of a finite set with a Zariski closed set. The approach requires certain auxiliary results guaranteeing embeddings of factor rings into direct products of simple modules. Analysis of these embeddings mimics earlier work of the first author and Zimmermann-Huisgen on products of torsion modules.
dc.description10 pages; AMS-TeX
dc.identifierhttps://arxiv.org/abs/math/0507551
dc.identifierhttp://arxiv.org/abs/math/0507551
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75909
dc.subjectRings and Algebras
dc.subjectQuantum Algebra
dc.subject16D60, 16P40
dc.titleThe Closed-Point Zariski Topology for Irreducible Representations
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