On locally finite alternative division rings with valuation (Q1093720)

This paper gives a new, easy proof of the known theorem that a locally finite complete alternative division ring with a valuation is a field. The prior proof used the theorem of Bruck and Kleinfeld which classifies all alternative division rings with IP. As a corollary it is shown that, if a locally finite triangle building is Moufang, then it is Desarguesian, i.e. classical.