Abstract
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.
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© 2004 Springer Science+Business Media New York
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Kiyek, K., Vicente, J.L. (2004). Valuation Theory. In: Resolution of Curve and Surface Singularities. Algebras and Applications, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2029-2_1
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DOI: https://doi.org/10.1007/978-1-4020-2029-2_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6573-5
Online ISBN: 978-1-4020-2029-2
eBook Packages: Springer Book Archive