Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T02:51:45.197Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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