交换环上赋值的合成

研究交换环上(Manis)赋值的合成。对于交换环R的一个赋值v及其值群的一个孤立子群Δ,定义了所谓的ν关于Δ所诱导的第一赋值和第二赋值,由此建立有关这两个诱导的赋值的一些结果。作为另一个主要结果,证明了对于交换环R上一个赋值u以及u的剩余环上一个核为零的赋值w,存在R上唯一的赋值v,使得u和w分别等价于v关于Δ所诱导的第一赋值和第二赋值,其中Δ是v的值群的某个孤立子群。此外,所合成的赋值v的实性被获得研究,由此获得了赋值v为实赋值的一个充分必要条件。

Composition of valuations on comutative ring

This paper aims to investigate the composition of(Manis) valuations on a(commutative) ring.For a valuation v on a commutative ring R and an isolated subgroup Δ of the value group of v,the so-called first and second valuations induced by v with Δ were defined,where Δ is an isolated subgroup of the value group of v.Several results were obtained on the induced valuations.Another important result was that for a valuation v on a ring R and a valuation w with null core on the residue ring of v,it existed a unique valuation v on R such that the first and second valuations induced by v with Δ were equivalent to u and w,respectively.The reality of this composed valuation v was also investigated,and a necessary and sufficient condition for v to be a real valuation was obtained.