Geodesic
Notes on Local Integral Extension Domains
Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 95-101

Voir la notice de l'article provenant de la source Cambridge University Press

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)). 
Jr., L. J. Ratliff. Notes on Local Integral Extension Domains. Canadian journal of mathematics, Tome 30 (1978) no. 1, pp. 95-101. doi: 10.4153/CJM-1978-008-4
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