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 | References | Similar Articles | Additional Information
Abstract: We prove the equivalence of the direct summand conjecture and descent of flatness for integral extensions.
- 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 308104, https://doi.org/10.1007/BF01390094
platification
d'un module, Inventions Math. 13 (1971), 1--89. Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13B99
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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
