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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A note on flat algebras
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by Augusto Nobile PDF
Proc. Amer. Math. Soc. 64 (1977), 206-208 Request permission

Abstract:

The following results are proved. If $f:A \to B$ is a homomorphism of rings, with B noetherian, I is an ideal of B contained in the Jacobson radical, and $B/{I^n}$ is A-flat, for all n, then f is flat. If, using similar notations and assumptions, I is generated by a regular sequence, then the flatness of B/I implies the flatness of f. A simple geometric application is given.
References
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 206-208
  • MSC: Primary 14C20; Secondary 13A15
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0498548-4
  • MathSciNet review: 0498548