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Proceedings of the American Mathematical Society

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Injective modules under flat base change


Author: Hans-Bjørn Foxby
Journal: Proc. Amer. Math. Soc. 50 (1975), 23-27
MSC: Primary 13C10
DOI: https://doi.org/10.1090/S0002-9939-1975-0409439-7
MathSciNet review: 0409439
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Abstract: It is proved that an injective module after a flat change of base is of pointwise finite injective dimension if and only if all the fibers at points associated to the injective module are Gorenstein rings (or trivial).


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

  • [1] H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8-28. MR 27 #3669. MR 0153708 (27:3669)
  • [2] I. Beck, $ \Sigma $-injective modules, J. Algebra 21 (1972), 232-249. MR 0357499 (50:9967)
  • [3] L. Claborn and R. Fossum, Class groups of $ n$-noetherian rings, J. Algebra 10 (1968), 263-285. MR 39 #5541. MR 0244224 (39:5541)
  • [4] H. Matsumura, Commutative algebra, Benjamin, New York, 1970. MR 42 #1813. MR 0266911 (42:1813)
  • [5] R. Hartshorne, Residues and duality, Lecture Notes in Math., no. 20, Springer-Verlag, Berlin and New York, 1966. MR 36 #5145. MR 0222093 (36:5145)
  • [6] D. Lazard, Épimorphismes plats d'anneaux, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A314-A316. MR 39 #l97c. MR 0238835 (39:197c)
  • [7] M. Raynaud, Anneaux locaux henseliens, Lecture Notes in Math., vol. 169, Springer-Verlag, Berlin and New York, 1970. MR 43 #3252. MR 0277519 (43:3252)

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DOI: https://doi.org/10.1090/S0002-9939-1975-0409439-7
Article copyright: © Copyright 1975 American Mathematical Society

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