Topologies on the torsion-theoretic spectrum of a noncommutative ring

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Let R-sp be the collection of all prime torsion theories on the category of left R-modules over an associative ring R. Three topologies - the order topology, the finitary order topology, and the reverse order topology (in the case that R is left noetherian) - are defined on R-sp and each is shown to exhibit some properties of the Zariski topology on the spectrum of a commutative ring. A fourth topology — the Gillman topology - is defined on E-sp when R is left noetherian and is used to characterize the separation of the reverse order topology.

Original languageEnglish
Pages (from-to)439-450
Number of pages12
JournalPacific Journal of Mathematics
Issue number2
StatePublished - Apr 1974
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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