The Nilpotence of the τ-Closed Prime Radical in Rings with τ-Krull Dimension

Necessary and sufficient conditions are provided for the nilpotence of the intersection of all τ-closed prime ideals of a ring R with τ-Krull dimension, where τ denotes a hereditary torsion theory on the category Mod-R of right R-modules. It is shown that these conditions hold, in particular, when τ...

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Bibliographic Details
Published inJournal of algebra Vol. 229; no. 2; pp. 498 - 513
Main Authors Albu, Toma, Krause, Günter, Teply, Mark L.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.07.2000
Subjects
associated prime ideal
hereditary torsion theory
prime radical
relative Krull dimension
relative nilpotence
τ-torsionfree module
τ-torsionfree module
hereditary torsion theory
relative nilpotence
prime radical
relative Krull dimension
associated prime ideal
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Summary:Necessary and sufficient conditions are provided for the nilpotence of the intersection of all τ-closed prime ideals of a ring R with τ-Krull dimension, where τ denotes a hereditary torsion theory on the category Mod-R of right R-modules. It is shown that these conditions hold, in particular, when τ is ideal invariant. Furthermore, conditions are provided for Ass(M) to be non-empty for every τ-torsionfree right R-module M≠0.
ISSN:0021-8693
1090-266X
DOI:10.1006/jabr.1999.8119