Torsion theories over semiperfect rings

Rutter, Edgar A.

doi:10.1090/S0002-9939-1972-0297819-X

Torsion theories over semiperfect rings
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by Edgar A. Rutter

Proc. Amer. Math. Soc. 34 (1972), 389-395

DOI: https://doi.org/10.1090/S0002-9939-1972-0297819-X

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Abstract:

In this note we characterize those torsion theories over a semiperfect ring such that the class of torsion free modules is closed under projective covers and the hereditary torsion theories for which this is true of the class of torsion modules. These results are applied to determine all hereditary torsion theories over an injective cogenerator ring with the property that the torsion submodule of every module is a direct summand.

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