Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-16T05:22:44.346Z Has data issue: false hasContentIssue false

Rings whose modules form few torsion classes

Published online by Cambridge University Press:  17 April 2009

B.J. Gardner
Affiliation:
The University of Tasmania, Hobart, Tasmania.
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.

Characterizations are obtained of rings R such that the only torsion classes (respectively, hereditary torsion classes) of left unital R-modules are {0} and the class of all modules.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Andrunakievič, V.A. and Rjabuhin, Ju.M., “Nadnil'potentnye i podydempotentnye radikaly algebr i radikaly modulei”, Mat. Issled. 3 (1968), 515.Google Scholar
[2]Bass, Hyman, “Finitistic dimension and a homological generalization of semi-primary rings”, Trans. Amer. Math. Soc. 95 (1960), 466488.CrossRefGoogle Scholar
[3]Dickson, Spencer E., “A torsion theory for abelian categories”, Trans. Amer. Math. Soc. 121 (1966), 223235.CrossRefGoogle Scholar
[4]Jacobson, Nathan, Structure of rings (Colloquium Publ. 37, revised ed., Amer. Math. Soc., Providence, Rhode Island, 1964).Google Scholar
[5]Jans, J.P., “Some aspects of torsion”, Pacific J. Math. 15 (1965), 12491259.CrossRefGoogle Scholar
[6]Năstăsescu, Constantin and Popescu, Nicolae, “Anneaux semi-artiniens”, Bull. Soc. Math. France 96 (1968), 357368.CrossRefGoogle Scholar
[7]Renault, Guy, “Sur les anneaux A, tels que tout A-module à gauche non nul contient un sous-module maximal”, C.R. Aaad. Sci. Parie Sér. A-B 264 (1967), A622–A624Google Scholar