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The cancellation property for modules

Part of the Lecture Notes in Mathematics book series (LNM,volume 246)

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References

  1. P. M. Cohn, The complement of a finitely generated direct summand of an abelian group. Proc. Amer. Math. Soc. 7 (1956), 520–521.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. P. Crawley, The cancellation of torsion abelian groups in direct sums, J. Algebra 2 (1965), 432–442.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. L. Fuchs, On quasi-injective modules, Annali Scuola Normale Sup. Pisa 23 (1969), 541–546.

    MathSciNet  MATH  Google Scholar 

  4. L. Fuchs, On a substitution property of modules, Monatshefte f. Math. 75(1971).

    Google Scholar 

  5. L. Fuchs and F. Loonstra, On the cancellation of modules in direct sums over Dedekind domains, Indagationes Math. 33 (1971), 163–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. R. Hirshon, On cancellation in groups, Amer. Math. Monthly 76 (1969), 1037–1039.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. C. S. Hsü, Theorems on direct sums of modules, Proc. Amer. Math. Soc. 13 (1962), 540–542.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. B. Jónsson and A. Tarski, Direct decompositions of finite algebraic systems, Notre Dame Math. Lectures, No. 5 (1947).

    Google Scholar 

  9. I. Kaplansky, Infinite abelian groups (Ann Arbor, 1969).

    Google Scholar 

  10. G. Kolettis, Homogeneously decomposable modules, Studies on Abelian Groups, Symposium, Montpellier 1967, 223–238.

    Google Scholar 

  11. S. Mac Lane, Homology (New York, 1963).

    Google Scholar 

  12. J. Rotman and T. Yen, Modules over a complete valuation ring, Trans. Amer. Math. Soc. 98 (1961), 242–254.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. W. V. Vanconcelos, Ideals and cancellations, Math. Zeitschr. 102 (1967), 353–355.

    CrossRef  Google Scholar 

  14. E. A. Walker, Cancellation in direct sums of groups, Proc. Amer. Math. Soc. 7 (1956), 898–902.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. R. B. Warfield, Jr., A Krull-Schmidt theorem for infinite sums of modules, Proc. Amer. Math. Soc. 22 (1969), 460–465.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. R. B. Warfield, Jr., Exchange rings and decompositions of modules, to appear.

    Google Scholar 

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© 1972 Springer-Verlag

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Fuchs, L. (1972). The cancellation property for modules. In: Lectures on Rings and Modules. Lecture Notes in Mathematics, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059566

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  • DOI: https://doi.org/10.1007/BFb0059566

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  • Print ISBN: 978-3-540-05760-4

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