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Ziegler spectra of serial rings

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Abstract

In this paper we prove that the Ziegler spectra of all serial rings are sober. We then use this proof to give a general framework for computing and understanding the T0-quotients of Ziegler spectra of uniserial rings. Finally, we illustrate this technique by computing the T0-quotients of Ziegler spectra of all rank one uniserial domains.

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Author information

Authors and Affiliations

  1. Division of Mathematics, School of Science and Technologies, University of Camerino, Via Madonna delle Carceri 9, 62032, Camerino, Italy

    Lorna Gregory

  2. Belarusian State University, Minsk, Belarus

    Gena Puninski

Authors
  1. Lorna Gregory
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  2. Gena Puninski
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Corresponding author

Correspondence to Lorna Gregory.

Additional information

The first author acknowledges the support of EPSRC through Grant EP/K022490/1.

The second author died during the preparation of this article.

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Gregory, L., Puninski, G. Ziegler spectra of serial rings. Isr. J. Math. 229, 415–459 (2019). https://doi.org/10.1007/s11856-018-1808-8

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  • DOI: https://doi.org/10.1007/s11856-018-1808-8

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