The Prime Spectrum and the Extended Prime Spectrum of Noncommutative Rings
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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 wordsprime ideals spectral spaces
Mathematics Subject Classifications (2000)06E15 16D25
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