关于拟赋值环

On Quasi-valuation Rings

本文主要研究了文[1]中提出的一个尚未解决的问题,即:如果V_1,V_2是拟赋值环R上的两个赋值,V_1,V_2到商域F上的开拓不等价,则V_1,V_2在R上是否等价?对四类商域为代数数域的拟赋值环,完全解决了上述问题。

In this paper, we have discussed an unsolved problem in [1], which is that if v_1 and v_2 are two valuations on quasi—valuation ring R, the extensions of v_1 and v_2 on R's quotient field F aren't equivalent, whether are v_1 and v_2 equivalent on R? we have completely answered the problem by means of four kinds of quasi—valuatinn rings whose quotient fields are algebraic number fields.