Lokalkompakte Fastkörper

It is shown that every locally compact, disconnected nearfield (F,τ) possesses a non-archimedean, discrete valuation | |, which induces τ. The valuation nearring R of | | only has one maximal ideal P, and the quotient group R/P is finite. If the kernel K of F is infinite and if E is an infinite subfield of K, then R/P may be considered as a right vector space over the residue field of (E, | |). Based on this assumption the ramification index and the residual degree are introduced and studied.