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›› 2009, Vol. 26 ›› Issue (3): 289-295.DOI: 10.7523/j.issn.2095-6134.2009.3.001

• Research Articles •     Next Articles

Classification of valuations on surfaces

XU Ning   

  1. Graduate University of the Chinese Academy of Sciences,Beijing 100049,China
  • Received:2008-03-21 Revised:2008-07-01 Online:2009-05-15

Abstract:

By letting K be a finitely generated field extension of k and v be a k-valuation of K, we define the height of the valuation. Based on this we obtain the complete classification of valuations on surfaces. In addition, we get the relationship between the valuation and transcendental power series.

Key words: valuation, height, rank, totally ordered group, transcendental power series

CLC Number: