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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

When is a flat algebra of finite type?


Author: Peter Schenzel
Journal: Proc. Amer. Math. Soc. 109 (1990), 287-290
MSC: Primary 13E05; Secondary 14B25
MathSciNet review: 1000168
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Abstract: Let $ A$ denote a commutative Noetherian domain. For an intermediate ring $ A \subseteq B \subseteq {A_x}$ flat over $ A$, it is shown that $ B$ is an $ A$-algebra of finite type. This is followed by an intrinsic description of the flatness of $ B$ over $ A$ and the asymptotic behavior of certain prime divisors. As an application, flat ideal-transforms are characterized.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1000168-6
PII: S 0002-9939(1990)1000168-6
Keywords: Intermediate ring, flat algebra, algebra of finite type, prime divisor, ideal-transform, affine scheme
Article copyright: © Copyright 1990 American Mathematical Society