Valuation Theory

  • K. Kiyek
  • J. L. Vicente
Part of the Algebras and Applications book series (AA, volume 4)


In this chapter we study valuation rings and valuations. We start with the concept of a Manis valuation of a ring K; Manis valuations behave nicely if K is a ring having large Jacobson radical. We show that a Manis valuation of K gives rise to a Manis valuation ring of K and that, conversely, every Manis valuation ring of K determines a Manis valuation of K. Also, for discrete Manis valuations we prove an approximation theorem.


Prime Ideal Maximal Ideal Valuation Ring Regular Element Residue Field 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • K. Kiyek
    • 1
  • J. L. Vicente
    • 2
  1. 1.Department of MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Departamento de AlgebraUniversidad de SevillaSevillaSpain

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