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Proceedings of the American Mathematical Society

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Direct summand conjecture
and descent for flatness


Author: Takeo Ohi
Journal: Proc. Amer. Math. Soc. 124 (1996), 1967-1968
MSC (1991): Primary 13B99
DOI: https://doi.org/10.1090/S0002-9939-96-03270-4
MathSciNet review: 1317044
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Abstract: We prove the equivalence of the direct summand conjecture and descent of flatness for integral extensions.


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

  • 1. Melvin Hochster, Topics in the homological theory of modules over commutative rings, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Nebraska, Lincoln, Neb., June 24–28, 1974; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 24. MR 0371879
  • 2. Melvin Hochster, Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 (1983), no. 2, 503–553. MR 723406, https://doi.org/10.1016/0021-8693(83)90092-3
  • 3. Michel Raynaud and Laurent Gruson, Critères de platitude et de projectivité. Techniques de “platification” d’un module, Invent. Math. 13 (1971), 1–89 (French). MR 0308104, https://doi.org/10.1007/BF01390094

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Additional Information

Takeo Ohi
Affiliation: Department of Mathematics, Science University of Tokyo, Shinjuku-ku, Tokyo 162, Japan

DOI: https://doi.org/10.1090/S0002-9939-96-03270-4
Received by editor(s): August 18, 1994
Received by editor(s) in revised form: December 21, 1994
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society