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Hereditary Torsion Theories for Noetherian Rings

  • Bo Stenström
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 217)

Abstract

For a commutative noetherian ring we have proved that every Gabriel topology ℑ arises from a set p of prime ideals as
$$ \\\mathfrak{F} = \{ a|a \not\subset \mathfrak{p},all\mathfrak{p} \in p\} ] $$
(Cor. VI.6.15). In the case of a non-commutative right noetherian ring the situation is not quite so simple. The main result of this chapter (Theorem 3.4) shows, however, that there is a large class of right noetherian rings for which the Gabriel topologies are uniquely determined by the prime ideals they contain. An important tool for obtaining this result is the non-commutative theory of associated prime ideals.

Keywords

Prime Ideal Prime Ring Noetherian Ring Torsion Module Minimal Prime Ideal 
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 1975

Authors and Affiliations

  • Bo Stenström
    • 1
  1. 1.Matematiska InstitutionenStockholms UniversitetSweden

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