A right PCI ring is right Noetherian
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- by Robert F. Damiano PDF
- Proc. Amer. Math. Soc. 77 (1979), 11-14 Request permission
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
- John Cozzens and Carl Faith, Simple Noetherian rings, Cambridge Tracts in Mathematics, No. 69, Cambridge University Press, Cambridge-New York-Melbourne, 1975. MR 0396660
- Lawrence Levy, Torsion-free and divisible modules over non-integral-domains, Canadian J. Math. 15 (1963), 132–151. MR 142586, DOI 10.4153/CJM-1963-016-1
- B. L. Osofsky, Noninjective cyclic modules, Proc. Amer. Math. Soc. 19 (1968), 1383–1384. MR 231857, DOI 10.1090/S0002-9939-1968-0231857-7
- Bo Stenström, Rings of quotients, Die Grundlehren der mathematischen Wissenschaften, Band 217, Springer-Verlag, New York-Heidelberg, 1975. An introduction to methods of ring theory. MR 0389953
Additional Information
- © Copyright 1979 American Mathematical Society
- 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