Algebra pp 519-537 | Cite as

Torsion Theories, Radicals, and Idempotent, Topologizing, and Multiplicative Sets

  • Carl Faith
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 190)


This chapter contains applications of the localizing functors, and quotient categories defined in the preceding chapter. The application 16.9 is to multiplicative subsets S of a ring R, and the corresponding (partial) ring of quotients R s with respect to S. Theorem 16.12 yields the Johnson maximal right quotient ring \(\widehat R\) of a right neat ring R (cf. Chapter 19). When R is semiprime, and satisfies the \({(acc)^ \bot }\) and (acc)⊕, then \(\widehat R\) is the classical right quoring.


Full Subcategory Torsion Module Abelian Category Quotient Ring Left Adjoint 
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Copyright information

© Springer-Verlag, Berlin · Heidelberg 1973

Authors and Affiliations

  • Carl Faith
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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