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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Direct summand conjecture and descent for flatness
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by Takeo Ohi PDF
Proc. Amer. Math. Soc. 124 (1996), 1967-1968 Request permission

Abstract:

We prove the equivalence of the direct summand conjecture and descent of flatness for integral extensions.
References
  • Melvin Hochster, Topics in the homological theory of modules over commutative rings, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 24, 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. MR 0371879, DOI 10.1090/cbms/024
  • Melvin Hochster, Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 (1983), no. 2, 503–553. MR 723406, DOI 10.1016/0021-8693(83)90092-3
  • 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 308104, DOI 10.1007/BF01390094
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Additional Information
  • Takeo Ohi
  • Affiliation: Department of Mathematics, Science University of Tokyo, Shinjuku-ku, Tokyo 162, Japan
  • Received by editor(s): August 18, 1994
  • Received by editor(s) in revised form: December 21, 1994
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 1996 American Mathematical Society
  • 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