When is a flat algebra of finite type?

Schenzel, Peter

doi:10.1090/S0002-9939-1990-1000168-6

When is a flat algebra of finite type?
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Proc. Amer. Math. Soc. 109 (1990), 287-290 Request permission

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.

References

Algèbre commutative

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