Asim Naseem and Angel Popescu: Extensions of discrete finite rank valued fields, p.245-252

Abstract:

We provide some sufficient conditions for a valued subfield $(K^{\prime },v^{\prime})$ of a valued field $(K,v)$ to be of finite codimension in $K,$ i.e. $[K:K^{\prime}]$ be finite. Moreover, these conditions on $K^{\prime}$ imply the fundamental equality $ef=[K:K^{\prime}]$ and the unicity of the valuation $v$ as an extension of $v^{\prime}$.

Key Words: Valued fields, general valuations, the fundamental equality, complete fields.

2000 Mathematics Subject Classification: Primary: 12J10,12J20,
Secondary: 13A18.

Download the paper in pdf format here.