On the Comparison of Rees's Valuations Over a Quasi-Unmixed Local Ring

Beddani, Charef

doi:10.1080/00927872.2013.820735

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An Equality Between the Number Of Minimal Primes In The Comp1

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2015

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“…Hence S is integrally closed [10, p. 185]. Therefore the hypotheses of the previous proposition are satisfied, 3 and from this we obtain the equality (16). 2…”

Section: An Equality Between the Number Of Minimal Primes In The Compmentioning

confidence: 81%

Some results on quasi-unmixed local domains

Beddani

Spivakovsky

2015

Journal of Algebra

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Available online xxxx Communicated by Steven Dale Cutkosky MSC: 13B35 13B22 13A18 Keywords: Divisorial valuations Quasi-unmixed local domainsThis paper shows that if (R, m) is a Noetherian unibranch local domain with field of fractions K, then the integral closure S of R in K is analytically irreducible and finite over R if and only if R is analytically irreducible. We also prove the equality between the number of minimal prime ideals in R and the number of maximal ideals in S in the case when R is a Noetherian quasi-unmixed local domain such that S is finite over R and S n has only one minimal prime for all the maximal ideals n in S, where S n is the n-adic completion of S n .

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“…Hence S is integrally closed [10, p. 185]. Therefore the hypotheses of the previous proposition are satisfied, 3 and from this we obtain the equality (16). 2…”

Section: An Equality Between the Number Of Minimal Primes In The Compmentioning

confidence: 81%