A characterization of left semiartinian rings

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In defining the torsion-theoretic Krull dimension of an associative ring R we make use of a function δ from the complete lattice of all subsets of the torsion-theoretic spectrum of R to the complete lattice of all hereditary torsion theories on R-mod. In this note we give necessary and sufficient conditions for δ to be injective, surjective, and bijective. In particular, δ is bijective if and only if R is a left semiartinian ring.

Original languageEnglish
Pages (from-to)425-428
Number of pages4
JournalBulletin of the Australian Mathematical Society
Issue number3
StatePublished - Dec 1974

ASJC Scopus subject areas

  • General Mathematics


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