Semilocal Rings and the Jacobson Radical

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


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.)


Prime Ideal Local Ring Primary Ring Ring Theory Endomorphism Ring 
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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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