On the closedness of singular loci
Masayoshi Nagata (1959)
Publications Mathématiques de l'IHÉS
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Masayoshi Nagata (1959)
Publications Mathématiques de l'IHÉS
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Hagen Knaf, Franz-Viktor Kuhlmann (2005)
Annales scientifiques de l'École Normale Supérieure
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Hani A. Khashan, H. Al-Ezeh (2007)
Archivum Mathematicum
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All rings considered in this paper are assumed to be commutative with identities. A ring is a -ring if every ideal of is a finite product of primary ideals. An almost -ring is a ring whose localization at every prime ideal is a -ring. In this paper, we first prove that the statements, is an almost -ring and is an almost -ring are equivalent for any ring . Then we prove that under the condition that every prime ideal of is an extension of a prime ideal of , the ring ...
Veronique Lierde (2011)
Open Mathematics
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Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate...
Steven Dale CUTKOSKY (2005)
Annales de l’institut Fourier
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Suppose that are regular local rings which are essentially of finite type over a field of characteristic zero. If is a valuation ring of the quotient field of which dominates , then we show that there are sequences of monoidal transforms (blow ups of regular primes) and along such that is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties. ...