关于模上赋值的分解  

Decomposition of valuations on module

作　　者：曾广兴[1] 郑建平[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2011年第5期409-416,共8页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(10761006)

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。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.

关 键 词：模 赋值 融洽的等价关系 Manis赋值 孤立子群 

分 类 号：O153.5[理学—数学]