Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1990-1000168-6
MathSciNet review: 1000168
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [B] N. Bourbaki, Algèbre commutative, Hermann, Paris, 1961, Chap. 4.
  • [E] P. M. Eakin, Jr., W. Heinzer, D. Katz, and L. J. Ratliff, Jr., Note on ideal-transforms, Rees rings, and Krull rings, J. Algebra 110 (1987), 407-419. MR 910391 (88h:13007)
  • [H] R. Hartshorne, Algebraic geometry, Springer-Verlag, New York, Heidelberg, and Berlin, 1977. MR 0463157 (57:3116)
  • [M] H. Matsumura, Commutative algebra, 2nd ed., Benjamin, New York, 1980. MR 575344 (82i:13003)
  • [R] F. Richman, Generalized quotient rings, Proc. Amer. Math. Soc. 16 (1965), 794-799. MR 0181653 (31:5880)
  • [S] P. Schenzel, Flatness and ideal-transforms of finite type, (to appear). MR 1068325 (91i:13011)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13E05, 14B25

Retrieve articles in all journals with MSC: 13E05, 14B25


Additional Information

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

American Mathematical Society