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Notes on Local Integral Extension Domains

Published online by Cambridge University Press:  20 November 2018

L. J. Ratliff Jr.
L. J. Ratliff Jr.*
Affiliation:
University of California, Riverside, California
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All rings in this paper are assumed to be commutative with identity, and the undefined terminology is the same as that in [3].

In 1956, in an important paper [2], M. Nagata constructed an example which showed (among other things): (i) a maximal chain of prime ideals in an integral extension domain R' of a local domain (R, M) need not contract in R to a maximal chain of prime ideals; and, (ii) a prime ideal P in R' may be such that height P < height P ∩ R. In his example, Rf was the integral closure of R and had two maximal ideals. In this paper, by using Nagata's example, we show that there exists a finite local integral extension domain of D = R[X](M,X) for which (i) and (ii) hold (see (2.8.1) and (2.10)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 95 - 101
Copyright
Copyright © Canadian Mathematical Society 1978

References

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