Notes on Local Integral Extension Domains
1978 ◽
Vol 30
(01)
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pp. 95-101
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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)).
2007 ◽
Vol 75
(3)
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pp. 417-429
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2018 ◽
Vol 85
(3-4)
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pp. 356
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1991 ◽
Vol 43
(2)
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pp. 233-239
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2010 ◽
Vol 83
(1)
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pp. 130-137
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2004 ◽
Vol 03
(04)
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pp. 437-443
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2017 ◽
Vol 163
(2)
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pp. 289-299
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Keyword(s):
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