Advertisement

Israel Journal of Mathematics

, Volume 23, Issue 2, pp 132–136 | Cite as

Torsion-free covers II

  • Mark L. Teply
Article

Abstract

This paper continues the study of the existence of torsion-free covers with respect to a faithful hereditary torsion theory (ℑ,F) of left modules over a ringR with unity. If the filter of left ideals associated with (ℑ,F) has a cofinal subset of finitely generated left ideals, then every leftR-module has a torsion-free cover. An example is given to illustrate how this result generalizes all previously known existence theorems for torsion-free covers.

Keywords

Left Ideal Injective Module Semiprime Ring Torsion Theory Left Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Banaschewski,On coverings of modules, Math. Nachr.31 (1966), 57–71.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    T. Cheatham,Finite dimensional torsion free rings, Pacific J. Math.39 (1971), 113–118.MathSciNetGoogle Scholar
  3. 3.
    E. Enochs,Torsion free covering modules, Proc. Amer. Math. Soc.14 (1963), 884–889.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    E. Enochs,Torsionfree covering modules II, Arch. Math. (Basel)22 (1971), 37–52.MATHMathSciNetGoogle Scholar
  5. 5.
    J. S. Golan,Localization of noncommutative rings, Comm. Pure Appl. Math.30 (1975).Google Scholar
  6. 6.
    J. S. Golan and M. L. Teply,Torsion-free covers, Israel J. Math.15 (1973), 237–256.MATHMathSciNetGoogle Scholar
  7. 7.
    B. Stenström,Rings and Modules of Quotients, Lecture Notes in Mathematics 237, Springer-Verlag, New York, 1971.MATHGoogle Scholar
  8. 8.
    M. L. Teply,Torsionfree injective modules, Pacific J. Math.28 (1969), 441–453.MATHMathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press of Israel 1976

Authors and Affiliations

  • Mark L. Teply
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleU.S.A.

Personalised recommendations