Displaying similar documents to “Formal prime ideals of infinite value and their algebraic resolution”

Conditions under which R ( x ) and R x are almost Q-rings

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 R is a Q -ring if every ideal of R is a finite product of primary ideals. An almost Q -ring is a ring whose localization at every prime ideal is a Q -ring. In this paper, we first prove that the statements, R is an almost Z P I -ring and R [ x ] is an almost Q -ring are equivalent for any ring R . Then we prove that under the condition that every prime ideal of R ( x ) is an extension of a prime ideal of R , the ring R ...

One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal

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...

Local monomialization of transcendental extensions

Steven Dale CUTKOSKY (2005)

Annales de l’institut Fourier

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Suppose that R S are regular local rings which are essentially of finite type over a field k of characteristic zero. If V is a valuation ring of the quotient field K of S which dominates S , then we show that there are sequences of monoidal transforms (blow ups of regular primes) R R 1 and S S 1 along V such that R 1 S 1 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. ...