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A characterization of left semiartinian rings

Published online by Cambridge University Press:  17 April 2009

Jonathan S. Golan
Jonathan S. Golan
Affiliation:
Department of Mathematics, University of Haifa, Mt Carmel, Haifa, Israel.
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Abstract

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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.

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

References

[1]Golan, Jonathan S., “A Krull-like dimension for noncommutative rings”, Israel J. Math. (to appear).Google Scholar
[2]Goldman, Oscar, “Rings and modules of quotients”, J. Algebra 13 (1969), 10–47.CrossRefGoogle Scholar