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Proceedings of the American Mathematical Society

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A right PCI ring is right Noetherian


Author: Robert F. Damiano
Journal: Proc. Amer. Math. Soc. 77 (1979), 11-14
MSC: Primary 16A46
DOI: https://doi.org/10.1090/S0002-9939-1979-0539620-1
MathSciNet review: 539620
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Abstract: C. Faith and J. Cozzens have shown that a ring, whose right proper cyclic modules are injective, is either semisimple or a simple, right semihereditary, right Ore V-domain. They have posed a question as to whether such a ring is right noetherian. In this paper, an affirmative answer is given to that question. Moreover, necessary and sufficient conditions are given as to when a right PCI ring is left PCI.


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

  • [1] J. Cozzens and C. Faith, Simple noetherian rings, Cambridge Tracts in Math. and Math. Phys., University Press, Cambridge, 1975. MR 0396660 (53:522)
  • [2] L. Levy. Torsion-free and divisible modules over nonintegral domains, Canad. J. Math., 15 (1963), 132-157. MR 0142586 (26:155)
  • [3] B. Osofsky, Noninjective cyclic modules, Proc. Amer. Math. Soc. 19 (1968), 1383-1384. MR 0231857 (38:185)
  • [4] B. Stenström, Rings of quotients, Springer-Verlag, Berlin and New York, 1975. MR 0389953 (52:10782)

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DOI: https://doi.org/10.1090/S0002-9939-1979-0539620-1
Article copyright: © Copyright 1979 American Mathematical Society

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