Abstract
Valuation theory has its origin in Krull’s paper [Kru32]. This paper provided a basic introduction to valuation theory and established the principal relations between ring theory and the theory of partially ordered groups. One of the main advantages of valuation theory is its ability to handle both these algebraic systems. In this section we present only the rudiments of the valuation theory of fields and, in particular, those parts of the theory which will be indispensable for introducing the approximation theorems. The reader who is interested in this subject may find additional details in many books, such as [Gi172a], [LaM71] and [Rib68].
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© 1992 Springer Science+Business Media Dordrecht
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Alajbegović, J., Močkoř, J. (1992). Approximation Theorems for Valuations on Fields. In: Approximation Theorems in Commutative Algebra. Mathematics and Its Applications(East European Series), vol 59. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2716-5_1
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DOI: https://doi.org/10.1007/978-94-011-2716-5_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5204-7
Online ISBN: 978-94-011-2716-5
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