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Homomorphisms between cartesian powers of an abelian group

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Part of the Lecture Notes in Mathematics book series (LNM,volume 874)

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References

  1. Arnold, D.: Genera and direct sum decompositions of torsion free modules, pp. 197–218 in: Abelian Group Theory, Lecture Notes in Math. 616, Springer-Verlag 1977.

    Google Scholar 

  2. Arnold, D. and Lady, E.: Endomorphism rings and direct sums of torsion-free Abelian groups, Trans. Amer. Math. Soc. 211 (1975), 225–237.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Auslander, M.: Coherent functors, pp. 189–231 in: Proceedings of a Conference on Categorical Algebra (La Jolla 1965), Springer-Verlag 1966.

    Google Scholar 

  4. Bass, H.: Big projective modules are free, Illinois J. Math. 7 (1963), 24–31.

    MathSciNet  MATH  Google Scholar 

  5. Beaumont, R. and Pierce, R.: Torsion-free rings, Illinois J. Math. 5 (1961), 61–98.

    MathSciNet  MATH  Google Scholar 

  6. Cartan, H. and Eilenberg, S.: Homological Algebra, Princeton University Press, Princeton 1956.

    MATH  Google Scholar 

  7. Charles, B.: Méthodes topologiques en théorie des groupes Abéliens, pp. 29–42 in: Proceedings of a Colloquium on Abelian Groups (Tihany 1963), Akadémiai Kiadó, Budapest 1964.

    Google Scholar 

  8. Dugas, M. and Göbel, R.: Die Struktur kartesischer Produkte ganzer Zahlen modulo kartesische Produkte ganzer Zahlen, Math. Z. 168 (1979), 15–21.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Dugas, M. and Göbel, R.: Quotients of reflexive modules, Fund. Math. (to appear)

    Google Scholar 

  10. Eklof, P.: Set-theoretic Methods in Homological Algebra and Abelian Groups, Les Presses de l'Université de Montréal, Montréal 1980.

    Google Scholar 

  11. Fuchs, L.: Infinite Abelian Groups, Vol. II, Academic Press, New York 1973.

    MATH  Google Scholar 

  12. Huber, M.: On Cartesian powers of a rational group, Math. Z. 169 (1979), 253–259.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Huber, M. and Warfield, R.: On the torsion subgroup of Ext(A,G), Arch. Math. (Basel) 32 (1979), 5–9.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Lady, E.: Nearly isomorphic torsion free Abelian groups, J. Algebra 35 (1975), 235–238.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Levy, L.: Torsion-free and divisible modules over non-integral domains, Can. J. Math. 15 (1963), 132–151.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Murley, C.: The classification of certain classes of torsion-free Abelian groups, Pacific J. Math. 40 (1972), 647–665.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Nunke, R.: Modules of extensions over Dedekind rings, Illinois J. Math. 3 (1959), 222–241.

    MathSciNet  MATH  Google Scholar 

  18. Nunke, R.: On direct products of infinite cyclic groups, Proc. Amer. Math. Soc. 13 (1962), 66–71.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. Nunke, R.: Slender groups, Acta Sci. Math. Szeged 23 (1962), 67–73.

    MathSciNet  MATH  Google Scholar 

  20. Reiner, I.: Maximal Orders, Academic Press, London 1975.

    MATH  Google Scholar 

  21. Robson, J.: Idealizers and hereditary Noetherian prime rings, J. Algebra 22 (1972), 45–81.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Small, L.: Semihereditary rings, Bull. Amer. Math. Soc. 73 (1967), 656–658.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. Swan, R.: Projective modules over group rings and maximal orders, Ann. Math. 76 (1962), 55–61.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. Warfield, R.: Homomorphisms and duality of torsion-free groups, Math. Z. 107 (1968), 189–200.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. Warfield, R.: Extensions of torsion-free Abelian groups of finite rank, Arch. Math. (Basel) 23 (1972), 145–150.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. Warfield, R.: Cancellation of modules and groups and stable range of endomorphism rings, Pacific J. Math. (to appear)

    Google Scholar 

  27. Zassenhaus, H.: Orders as endomorphism rings of modules of the same rank, J. London Math. Soc. 42 (1967), 180–182.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1981 Springer-Verlag

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Huber, M., Warfield, R.B. (1981). Homomorphisms between cartesian powers of an abelian group. In: Göbel, R., Walker, E. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090536

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  • DOI: https://doi.org/10.1007/BFb0090536

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