摘要
设k是特征为零的域,k[x]为k上的多项式环,给出了k[x]上带权单项式导子的概念,然后通过对权是否为零进行分类讨论,证明了D是权为零的非零单项式导子当且仅当存在b∈k\{0},s∈N,使得对任意n∈N都有d(x^n)=nbx^(s+n-1);D是权为λ≠0的非零单项式导子当且仅当存在a∈k\{0},使得D(x^n)=0,n={0λ^(-1)((λa+1)~n-1)x^n,n≥1。
Monomial derivation with weight on k[x],the polynomial ring over characteristic zero filed k,is defined.Then the classification of this kind of derivations is established by discussing whether the weight is zero.More precisely,it is showed that Dis a nonzero monomial derivation with weight zero if and only if there exist b∈k/{0},s∈N,such that d(x-n)=nbx-(s+n-1) for all n∈N;It is also proved that Dis a nonzero monomial derivation with weight λ≠0 if and only if there exists a∈k/{0} such that D(x-n)=0,n={0λ-(-1)((λa+1)-n-1)x-n,n≥1
出处
《重庆师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2016年第5期63-66,共4页
Journal of Chongqing Normal University:Natural Science
基金
重庆人文科技学院教改项目(No.15CRKXJ05)
关键词
导子
权
多项式环
单项式
derivation
weight
polynomial ring
monomial