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Proceedings of the American Mathematical Society

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

 

 

A note on flat algebras


Author: Augusto Nobile
Journal: Proc. Amer. Math. Soc. 64 (1977), 206-208
MSC: Primary 14C20; Secondary 13A15
MathSciNet review: 0498548
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0498548-4
Keywords: Ring, flat algebra, regular sequence, relative Cartier divisor
Article copyright: © Copyright 1977 American Mathematical Society