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Semilocal Rings and the Jacobson Radical

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

Abstract

The main topics of this chapter are (1) the Jacobson radical of a ring and of a module 18.0; (2) the Perlis-Jacobson characterization 18.6 of the radical of a ring; (3) local rings 18.10; (4) semiprimary rings 18.12; (5) the theorem of Hopkins and Levitzki 18.13; (6) the Krull-Schmidt or Unique Decomposition Theorem 18.18; (7) the basic module and ring 18.21–23; (8) the Chinese remainder theorem 18.30–32 and primary decomposable rings 18.36–37; and (9) the characterization 18.47 of rings with semilocal right quorings. (As defined by (I, p. 4.10), R is semilocal if R/rad R is semisimple. Also see 18.10A.)

Keywords

Prime Ideal Local Ring Primary Ring Ring Theory Endomorphism 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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