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Abelian Group Theory pp 41–52Cite as

Abelian groups finitely generated over their endomorphism rings

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

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References

  1. D. M. Arnold, Strongly homogeneous torsion free abelian groups of finite rank, Proc. A. M. S., 56 (1976), 67–72.

    Article  MathSciNet  MATH  Google Scholar 

  2. D. M. Arnold, R. S. Pierce, J. D. Reid, C. Vinsonhaler, W. Wickless, Torsion free abelian groups of finite rank projective as modules over their endomorphism rings, J. Algebra, to appear.

    Google Scholar 

  3. R. A. Beaumont and R. S. Pierce, Subrings of algebraic number fields, Acta. Sci. Math. Szeged., 22 (1961), 202–216.

    MathSciNet  MATH  Google Scholar 

  4. __________, Torsion free rings, Ill.J. Math., 5 (1961), 61–98.

    MathSciNet  MATH  Google Scholar 

  5. M. C. R. Butler, On locally free torsion-free rings of finite rank, J. London Math. Soc., 43 (1968), 297–300.

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  7. G. P. Niedzwicki and J. D. Reid, Torsion free abelian groups cyclic projective over their endomorphism rings, to appear.

    Google Scholar 

  8. R. S. Pierce, Subrings of simple algebras, Michigan Math. J., 7 (1960).

    Google Scholar 

  9. J. D. Reid, Abelian groups cyclic over their endomorphism rings, to appear.

    Google Scholar 

  10. _____, On the ring of quasi-endomorphisms of a torsion free group, Topics in Abelian Groups (Proc. Sympos. New Mexico State University, 1962), Scott, Foresman, Chicago, Ill., 1963, pp. 51–68.

    Google Scholar 

  11. _____, On rings on groups, Pac. J. Math., 53 (1974), 229–237.

    Article  MATH  Google Scholar 

  12. P. Ribenboim, Modules sur un anneau de Dedekind, Summa Brasiliensis Math., 3 (1952), 21–36.

    MathSciNet  MATH  Google Scholar 

  13. P. Schultz, The endomorphism ring of the additive group of a ring, J. Austral. Math. Soc., 15 (1973) 60–69.

    Article  MathSciNet  MATH  Google Scholar 

  14. P. Schultz and R. Bowshell, Unital rings whose additive endomorphisms commute, Math. Ann., 228 (1977), 197–214.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. J. D. Reid
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Rüdiger Göbel Elbert Walker

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© 1981 Springer-Verlag

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Reid, J.D. (1981). Abelian groups finitely generated over their endomorphism rings. In: Göbel, R., Walker, E. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090522

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  • DOI: https://doi.org/10.1007/BFb0090522

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10855-9

  • Online ISBN: 978-3-540-38767-1

  • eBook Packages: Springer Book Archive

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