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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Decomposing overrings


Authors: B. Cortzen, L. W. Small and J. T. Stafford
Journal: Proc. Amer. Math. Soc. 82 (1981), 28-30
MSC: Primary 16A50; Secondary 16A62
DOI: https://doi.org/10.1090/S0002-9939-1981-0603595-6
MathSciNet review: 603595
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Abstract: We show that if $ S \supset R$ are rings such that $ {S_R}$ is projective, then $ {R_R}$ is a direct summand of $ {S_R}$ if and only if $ {S_R}$ is faithfully projective (this condition holds, in particular, if $ {S_R}$ is free).


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

  • [1] N. Bourbaki, Algèbre commutative, Chaps. I, II, Hermann, Paris, 1961.
  • [2] B. Cortzen, Finitistic dimension of ring extensions, (to appear). MR 654053 (83h:16034)
  • [3] T. Y. Lam, Serre's conjecture, Lecture Notes in Math., vol. 635, Springer-Verlag, Berlin and New York, 1978. MR 0485842 (58:5644)
  • [4] J. McConnell, On the global dimension of some rings, Math. Z. 153 (1977), 253-254. MR 0457498 (56:15703)
  • [5] J. T. Stafford, On the stable range of right Noetherian rings, Bull. London Math. Soc. (to appear). MR 599638 (82f:16017)

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DOI: https://doi.org/10.1090/S0002-9939-1981-0603595-6
Article copyright: © Copyright 1981 American Mathematical Society

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