线性J-Armendariz环  

Linear J-Armendariz Rings

作　　者：陈卫星[1] 

机构地区：[1]山东工商学院数学与信息科学学院,山东烟台264005

出　　处：《吉林大学学报（理学版）》2016年第3期401-407,共7页Journal of Jilin University:Science Edition

基　　金：山东省自然科学基金(批准号:ZR2013AL013;ZR2014AL001)

摘　　要：如果对任意的f(x)=a_0+a_1x,g(x)=b_0+b_1x∈R[x],f(x)g(x)=0蕴含所有a_ib_j∈J(R),则环R称为线性J-Armendariz环(简称LJA环).其中:i,j∈{0,1};J(R)是R的Jacobson根.考虑LJA环的性质及与其他相关环类的关系,给出了2-primal环的无限直积非2-primal环的简单例子,并证明了Koethe猜想有肯定解当且仅当任意NI环的多项式环是LJA环.A ring Ris called LJA ring if f（x）g（x）=0implies aibj∈J（R）for all f（x）=a0＋a1x,g（x）=b0＋b1xin 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 

分 类 号：O153.3[理学—数学]