Ziegler spectra of serial rings

Lorna Gregory; Gena Puninski

doi:10.1007/s11856-018-1808-8

Ziegler spectra of serial rings

Lorna Gregory, Gena Puninski

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	415-459
Number of pages	45
Journal	Israel Journal of Mathematics
Volume	229
Issue number	1
DOIs	https://doi.org/10.1007/s11856-018-1808-8
Publication status	Published - 1 Jan 2019

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10.1007/s11856-018-1808-8

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title = "Ziegler spectra of serial rings",

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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AB - 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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Ziegler spectra of serial rings

Abstract

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