关于交换环的V-赋值的几个结果

SVERAL RESULTS ON V-VALUATIONS OF COMMUTATIVE RINGS

定义了V-赋值的比较,给出了定理2·2:若Aω是关于Av的中间集,则(ω,Λ)≥(v,Γ)。研究了布尔V-幺半群,得到:若Γ为布尔V-幺半群,则(v,Γ)是形式有限的。证明了:设(B,M)为环R的非浅显Manis赋值对,则B为实环当且仅当R为实环。进一步,给出一个反例用来说明,命题2对于V-赋值对而言未必成立。

It is shown that if A_w is a intermediate subset to A_v,then (ω,Λ)≥(v,Γ).The Boolean V-monoids is studied,and a result is obtained as follows:Let (v,Γ) be a V-valuation of ring R.If is Boolean,then (v,Γ) is formally infinite.It is shown that if (B,M) is manis a valuation pair of a ring R,then B is formally real if R and only if R is formally real.Moreover,a counter-example is given to illustrate that Proposition 2 is false for V-valuation rings.