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A characterization of left semiartinian rings
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 425 - 428
- Copyright
- Copyright © Australian Mathematical Society 1974
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