Revista Matemática Iberoamericana

Proximity relations for real rank one valuations dominating a local regular ring

Ángel Granja and Cristina Rodríguez

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We study 0-dimensional real rank one valuations centered in a regular local ring of dimension $n\geq 2$ such that the associated valuation ring can be obtained from the regular ring by a sequence of quadratic transforms. We define two classical invariants associated to the valuation (the refined proximity matrix and the multiplicity sequence) and we show that are equivalent data of the valuation.

Article information

Rev. Mat. Iberoamericana, Volume 19, Number 2 (2003), 393-412.

First available in Project Euclid: 8 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13F30: Valuation rings [See also 13A18]
Secondary: 13H05: Regular local rings

valuation real rank regular ring quadratic transform


Granja, Ángel; Rodríguez, Cristina. Proximity relations for real rank one valuations dominating a local regular ring. Rev. Mat. Iberoamericana 19 (2003), no. 2, 393--412.

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