PI-代数的根扩张  

Radical extensions of PI-algebras

作　　者：游松发[1] 

机构地区：[1]湖北大学数学与计算机科学学院,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2011年第2期227-229,共3页Journal of Hubei University：Natural Science

摘　　要：研究PI-代数的根扩张所满足的多项式恒等式,找到了一类满足标准多项式恒等式的根扩张代数.得到下面定理:令A满足d次多项式恒等式f(x1,…,xd)=0,R是A的根扩张,且Nil(R)=0,则R满足标准多项式恒等式Sd(x1,…,xd)=0.Some polynomials of radical extensions on PI-algebras were investigated,and some radical extension algebras satisfying the standard polynomial identity were obtained,The follow theory was got.Let R be an algebra having no nonzero nil ideals and radical over a subalgebra A satisfying an identity f（x1,…,xd）=0 of degree d,and then R satisfied the stamdard polynomial identity Sd（x1,…,xd）=0.

关 键 词：根扩张 标准多项式恒等式 诣零根 JACOBSON根 半素 

分 类 号：O153.3[理学—数学]