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On the Complete Integral Closure of a Domain

For a given positive integer n, a semivaluation domain Dnis constructed so that the complete integral closure has to be applied successively exactly n times before obtaining a completely integrally closed domain. Letting Gnbe the group of divisibility of Dn, we set $G = \sum \boxplus G_n$ , the... Full description

1st Person: Hill, Paul
Source: in Proceedings of the American Mathematical Society Vol. 36, No. 1 (1972), p. 26-30
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Type of Publication: Article
Language: English
Published: 1972
Keywords: research-article
Online: Volltext
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003 DE-601
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008 150325s1972 000 0 eng d
024 7 |a 10.2307/2039031  |2 doi 
024 8 |a 2039031 
035 |a 2039031 
040 |b ger  |c GBVCP 
041 0 |a eng 
084 |a 13B20  |2 MSC 
084 |a 06A60  |2 MSC 
084 |a Complete integral closure  |2 MSC 
084 |a semivaluation  |2 MSC 
084 |a Bezout domain  |2 MSC 
084 |a group of divisibility  |2 MSC 
084 |a lattice ordered group  |2 MSC 
100 1 |a Hill, Paul 
245 1 0 |a On the Complete Integral Closure of a Domain  |h Elektronische Ressource 
300 |a Online-Ressource 
500 |a Copyright: Copyright 1972 American Mathematical Society 
520 |a For a given positive integer n, a semivaluation domain Dnis constructed so that the complete integral closure has to be applied successively exactly n times before obtaining a completely integrally closed domain. Letting Gnbe the group of divisibility of Dn, we set $G = \sum \boxplus G_n$ , the cardinal sum of the groups Gn. It is concluded that the semivaluation domain D having G as its group of divisibility is a Bezout domain with the property that $D \subset D^\ast \subset D^{\ast\ast} \subset D^{\ast\ast\ast} \subset \cdots$ is a strictly ascending infinite chain, where D*is the complete integral closure of D. 
653 |a research-article 
773 0 8 |i in  |t Proceedings of the American Mathematical Society  |d Providence, RI : Soc  |g Vol. 36, No. 1 (1972), p. 26-30  |q 36:1<26-30  |w (DE-601)JST068805667  |x 1088-6826 
856 4 1 |u https://www.jstor.org/stable/2039031  |3 Volltext 
856 4 1 |u http://dx.doi.org/10.2307/2039031  |3 Volltext 
912 |a GBV_JSTOR 
951 |a AR 
952 |d 36  |j 1972  |e 1  |h 26-30 

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