Algebras and Representation Theory

, Volume 10, Issue 3, pp 257–270 | Cite as

The Prime Spectrum and the Extended Prime Spectrum of Noncommutative Rings



We investigate the prime spectrum of a noncommutative ring and its spectral closure, the extended prime spectrum. We construct a ring for which the prime spectrum is a spectral space different from the extended prime spectrum and we construct a von Neumann regular ring for which the prime spectrum is not a spectral space.

Key words

prime ideals spectral spaces 

Mathematics Subject Classifications (2000)

06E15 16D25 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Ljubljana, IMFMLjubljanaSlovenia
  2. 2.Universität Regensburg, NWF I-MathematikRegensburgGermany

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