中文摘要：

研究交换环上模的赋值分解。设M是交换环R上一个模,v：M→Δ是M的一个赋值,且Γ是由v所诱导的值群。通过引进Δ上融洽的等价关系以及Γ的v-孤立子群,研究了Δ上融洽的等价关系Γ和的-孤立子群之间的密切关系。证明了如下主要结果：对于Γ的一个v-孤立子群∑,v可分解为M的一个新赋值—v以及—v所诱导的剩余环上一个核为零且值群为∑的Manis赋值。

英文摘要：

The purpose of this paper is to investigate the decomposition of valuations on a module over a commutative ring. Let M be a module over a commutative ring R,let v.M→Δ be a valuation on M,and let Γ be the value group induced by v. By introducing the notions of harmonic equivalences on A and v-isolated subgroups of Γ, the closed interplay of harmonic equivalences on A and v-isolated subgroups of Γ is investi- gated. A main result in this paper is established as follows： For a v-isolated subgroup ∑ of F,v can be decomposed into a new valuation on M and a Manis valuation with null core and value group ∑ on the residue class ring induced by this new valuation.