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Proceedings of the American Mathematical Society

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An uncountable Noetherian ring with free additive group


Author: John D. O’Neill
Journal: Proc. Amer. Math. Soc. 66 (1977), 205-207
MSC: Primary 20K20; Secondary 13E05
MathSciNet review: 0450426
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Abstract | References | Similar Articles | Additional Information

Abstract: An example is given of an uncountable Noetherian ring whose additive group is free. This answers a question posed indirectly by L. Fuchs.


References [Enhancements On Off] (What's this?)

  • [1] László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
  • [2] László Fuchs, Infinite abelian groups. Vol. II, Academic Press, New York-London, 1973. Pure and Applied Mathematics. Vol. 36-II. MR 0349869
  • [3] Paul Hill, On the splitting of modules and abelian groups, Canad. J. Math. 26 (1974), 68–77. MR 0338217

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0450426-2
Keywords: Free group, torsion-free group, pure independent set
Article copyright: © Copyright 1977 American Mathematical Society