Torsionfree projective modules

Teply, Mark L.

doi:10.1090/S0002-9939-1971-0271146-8

Torsionfree projective modules
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by Mark L. Teply

Proc. Amer. Math. Soc. 27 (1971), 29-34

DOI: https://doi.org/10.1090/S0002-9939-1971-0271146-8

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Abstract:

In this paper, the following condition for a torsion theory in the sense of S. E. Dickson is examined: ($\text {P}$) Every nonzero torsionfree module contains a nonzero projective submodule. A special relationship between condition ($\text {P}$) and Goldie’s torsion theory is shown; and the rings, for which every nontrivial torsion theory satisfies condition ($\text {P}$), are classified.

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