2021/11/20 by Kuhlmann, Franz-Viktor · 1 citation
#12J20 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 12J10 #Secondary 13A18
paper · doi:10.48550/arxiv.2111.10529
We introduce the notion of \it approximation type for the partial, and in certain cases the total description of extensions of a given valuation from a field K to the rational function field K(x). To every extension, a unique approximation type of x over K is associated, while x may be the limit of many pseudo Cauchy sequences. Approximation types also provide information in cases where the extensions are not immediate, and we prove that they correspond bijectively to the extensions when K is algebraically closed or lies dense in its algebraic closure.