吉林大学学报（理学版）2016，Vol.54Issue(3)：401-407,7.DOI:10.13413/j.cnki.jdxblxb.2016.03.01
线性 J-Armendariz 环
Linear J-Armendariz Rings
摘要
Abstract
A ring R is called LJA ring if f (x )g (x )=0 implies a ib j ∈J (R )for all f (x )=a 0 +a 1 x , g (x)=b 0 +b 1 x in R [x ]and i ,j = 0,1,where J (R )is the Jacobson radical of R.Considering the properties of LJA rings and the relationship between such rings and other related rings,the author gives simple examples of an infinite direct product of 2-primal rings not to be a 2-primal ring,and proves that Koethe’s conjecture has a positive solution if and only if a polynomial ring over any NI ring is an LJA ring.关键词
Armendariz 环/线性 Armendariz 环/线性 J-Armendariz 环Key words
Armendariz ring/linear Armendariz ring/linear J-Armendariz ring分类
数理科学引用本文复制引用
陈卫星..线性 J-Armendariz 环[J].吉林大学学报（理学版）,2016,54(3):401-407,7.基金项目
山东省自然科学基金(批准号:ZR2013AL013 （）
ZR2014AL001) （）
