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Noetherianity of the space of irreducible representations

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Abstract

LetR 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 leftR-modules (or, more generally, simple objects in a complete abelian category). Under this topology the points are closed, and whenR is left noetherian the corresponding topological space is noetherian. IfR is commutative (or PI, or FBN) the corresponding topological space is naturally homeomorphic to the maximal spectrum, equipped with the Zariski topology. WhenR 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.

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Authors and Affiliations

  1. Department of Mathematics, Temple University, 19122, Philadelphia, PA, USA

    Edward S. Letzter

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  1. Edward S. Letzter
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Correspondence to Edward S. Letzter.

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The author’s research was supported in part by NSF grants DMS-9970413 and DMS-0196236.

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Letzter, E.S. Noetherianity of the space of irreducible representations. Isr. J. Math. 136, 307–316 (2003). https://doi.org/10.1007/BF02807203

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  • DOI: https://doi.org/10.1007/BF02807203

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