# 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 in Proceedings of the American Mathematical Society Vol. 36, No. 1 (1972), p. 26-30 More Articles Article English 1972 research-article Volltext Volltext
LEADER 001 003 01829nma a2200373 c 4500 JST068968396 DE-601 20180529002837.0 cr uuu---uuuuu 150325s1972 000 0 eng d 7 |a 10.2307/2039031  |2 doi 8 |a 2039031 |a 2039031 |b ger  |c GBVCP 0 |a eng |a 13B20  |2 MSC |a 06A60  |2 MSC |a Complete integral closure  |2 MSC |a semivaluation  |2 MSC |a Bezout domain  |2 MSC |a group of divisibility  |2 MSC |a lattice ordered group  |2 MSC 1 |a Hill, Paul 1 0 |a On the Complete Integral Closure of a Domain  |h Elektronische Ressource |a Online-Ressource |a Copyright: Copyright 1972 American Mathematical Society |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. |a research-article 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 4 1 |u https://www.jstor.org/stable/2039031  |3 Volltext 4 1 |u http://dx.doi.org/10.2307/2039031  |3 Volltext |a GBV_JSTOR |a AR |d 36  |j 1972  |e 1  |h 26-30

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