Note on simple integral extension domains and maximal chains of prime ideals

Author:
L. J. Ratliff

Journal:
Proc. Amer. Math. Soc. **77** (1979), 179-185

MSC:
Primary 13B20; Secondary 13A15

DOI:
https://doi.org/10.1090/S0002-9939-1979-0542081-X

MathSciNet review:
542081

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Abstract: It is shown that if *R* is a semi-local (Noetherian) domain, then there exists a simple integral extension domain of *R* such that there exists a maximal chain of prime ideals of length *n* in some integral extension domain of *R* if and only if there exists a maximal chain of prime ideals of length *n* in . An interesting existence theorem on a certain type of height one prime ideals in follows.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1979-0542081-X

Keywords:
Integral extension ring,
maximal chain of prime ideals,
polynomial ring,
semi-local ring,
simple extension ring,
Upper Conjecture

Article copyright:
© Copyright 1979
American Mathematical Society