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Proceedings of the American Mathematical Society

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

 

 

Torsion theories over semiperfect rings


Author: Edgar A. Rutter
Journal: Proc. Amer. Math. Soc. 34 (1972), 389-395
MSC: Primary 16A62
DOI: https://doi.org/10.1090/S0002-9939-1972-0297819-X
MathSciNet review: 0297819
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0297819-X
Keywords: Hereditary torsion theory, splitting torsion theory, torsion-torsion free class, injective hull, projective cover, semiperfect ring, injective cogenerator ring
Article copyright: © Copyright 1972 American Mathematical Society