VALUATIONS DEFINED BY OSTROWSKI NETS

[摘要] Ostrowski proved that if v is a valuation on an algebraically closed field F and if w is a valuation extending v to the field F (x) of rational functions over F, then w is defined by a transcendental pseudo-convergent net (that is, an Ostrowski net) or w is a Rella extension of v centered about x - c for some c in F. In this paper, valuations on the field of rational functions over an arbitrary field determined by Ostrowski nets, along with the topologies they generate, are investigated.

[发布日期] 1993-12-13