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When Flats are Torsion Free

Published online by Cambridge University Press:  20 November 2018

S. Page
S. Page*
Affiliation:
Department of Mathematics, The University of British Columbia, Vancouver 8, British Columbia
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Given a complete Serre class τ this determines a torsion theory with T the class of torsion modules. It also determines the torsion free modules. For the classical torsion in the category of abelian groups the torsion free modules are flat and visa-versa. Which rings are characterized by this property? More precisely: Which rings admit a torsion theory for which the concepts of torsion free and flat are equivalent? We also dispose of the cases when R admits a toision theory for which torsion free is equivalent to injective and when projective is equivalent to torsion free.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 559 - 561
Copyright
Copyright © Canadian Mathematical Society 1974

References

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