The Prime Spectrum and the Extended Prime Spectrum of Noncommutative Rings

Author: Klep Igor   Tressl Marcus  

Publisher: Springer Publishing Company

ISSN: 1386-923X

Source: Algebras and Representation Theory, Vol.10, Iss.3, 2007-06, pp. : 257-270

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Abstract

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.