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

Filtration Dition 

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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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