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Semiprimitive Rings, Semiprime Rings, and the Nil Radical

  • Carl Faith
Chapter
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 191)

Abstract

A ring R is semiprime (semiprimitive) if and only the intersection of the prime (primitive) ideals is zero. Then, R is a subdirect product of prime (primitive) rings 26.6 and 26.13. The (McCoy) prime radical of a ring is defined to be the intersection of the prime ideals, and is characterized as the set of all strongly nilpotent elements of R (theorem of Levitzki 26.5). When R is commutative, this is just the set of nilpotent elements.

Keywords

Prime Ideal Prime Ring Nilpotent Element Subdirect Product Semiprime Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Carl Faith
    • 1
    • 2
  1. 1.Rutgers, The State UniversityNew BrunswickUSA
  2. 2.The Institute for Advanced StudyPrincetonUSA

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