Abstract
We first consider an arbitrary (not necessarily algebraic) field extension L∣K. Let A (resp. B) be a valuation ring of K (resp. L). We say that B lies over A if A = B ∩ K; in this case B is also called an extension of A. Considering A and B as local subrings of L we gets:
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(13.1)
B lies over A if and only if B dominates A.
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© 1972 Springer-Verlag Berlin Heidelberg
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Endler, O. (1972). Extension of Valuation Rings. In: Valuation Theory. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65505-0_3
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DOI: https://doi.org/10.1007/978-3-642-65505-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06070-3
Online ISBN: 978-3-642-65505-0
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