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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Torsionfree projective modules


Author: Mark L. Teply
Journal: Proc. Amer. Math. Soc. 27 (1971), 29-34
MSC: Primary 16.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0271146-8
MathSciNet review: 0271146
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Abstract: In this paper, the following condition for a torsion theory in the sense of S. E. Dickson is examined:

(P) Every nonzero torsionfree module contains a nonzero projective submodule.

A special relationship between condition (P) and Goldie's torsion theory is shown; and the rings, for which every nontrivial torsion theory satisfies condition (P), are classified.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0271146-8
Keywords: Ring, projective module, torsion theory, torsion, torsion-free, essential submodule, perfect ring, socle
Article copyright: © Copyright 1971 American Mathematical Society