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A module as a torsion-free cover

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Abstract

LetR be a ring, and let (ℐ, ℱ) be an hereditary torsion theory of leftR-modules. An epimorphism ψ:M→X is called a torsion-free cover ofX if (1)M∈ ℱ, (2) every homomorphism from a torsion-free module intoX can be factored throughM, and (3) ker ψ contains no nonzero ℐ -closed submodules ofM. Conditions onM andN are studied to determine when the natural mapsM→M/N andQ(M)→Q(M)/N are torsion-free covers, whenQ(M) is the localization ofM with respect to (ℐ, ℱ). IfM→M/N is a torsion-free cover andM is projective, thenN⊆radM. Consequently, the concepts of projective cover and torsion-free cover coincide in some interesting cases.

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References

  1. B. Banaschewski,On coverings of modules, Math. Nachr.31 (1966), 51–71.

    Article  MathSciNet  Google Scholar 

  2. T. Cheatham,The quotient field as a torsion-free covering module, Isr. J. Math.33 (1979), 172–176.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Enochs,Torsion free covering modules, Proc. Am. Math. Soc.14 (1963), 884–889.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Golan,Localization of Noncommutative Rings, Pure and Applied Math. Series 30, Marcel Dekker, New York, 1975.

    MATH  Google Scholar 

  5. J. Golan and M. Teply,Torsion-free covers, Isr. J. Math.15 (1973), 237–256.

    MATH  MathSciNet  Google Scholar 

  6. E. Matlis,The ring as a torsion-free cover, Isr. J. Math.37 (1980), 211–230.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Teply,Torsion-free injective modules, Pacific J. Math.28 (1969), 441–453.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Wichita State University, 67208, Wichita, KS, USA

    John J. Hutchinson & Mark L. Teply

  2. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    John J. Hutchinson & Mark L. Teply

Authors
  1. John J. Hutchinson
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  2. Mark L. Teply
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Hutchinson, J.J., Teply, M.L. A module as a torsion-free cover. Israel J. Math. 46, 305–312 (1983). https://doi.org/10.1007/BF02762890

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  • DOI: https://doi.org/10.1007/BF02762890

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