| Herstein定理的推广 |
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| 引用本文： | 傅昶林,杨新松,陈光海.Herstein定理的推广[J].数学学报,2003,46(2):261-268. |
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| 作者姓名： | 傅昶林 杨新松 陈光海 |
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| 作者单位： | 哈尔滨理工大学数学系,哈尔滨,150080 |
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| 基金项目： | 黑龙江省自然科学基金资助项目 |
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| 摘 要： | 1955年Herstein将著名的Jacobson定理推广为:定理A.如果对R中任意x,y,存在可依赖于x,y的整系数多项式p(t),使x-x2p(x),y]=0,则R是交换的.本文利用多项式的系数和定义了n元多项式,f(x1,x2…,xn)的Fk性质,并以此证明了一个环的交换性定理,当n=1时,即得到定理A.
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| 关 键 词： | 多项式的Fk性质 多项式的系数和 Herstein定理 |
| 文章编号： | 0583-1431(2003)02-0261-08 |
| 修稿时间： | 2001年10月31 |
A Generalization of Herstein's Theorem |
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| Chang Lin FU Xin Song YANG Guang Hai CHEN.A Generalization of Herstein''''s Theorem[J].Acta Mathematica Sinica,2003,46(2):261-268. |
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| Authors: | Chang Lin FU Xin Song YANG Guang Hai CHEN |
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| Institution: | Chang Lin FU Xin Song YANG Guang Hai CHEN(Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, P. R. China) |
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| Abstract: | Herstein generalized Jacobson's famous theorem on the commutativity of rings in 1955 as follows. Theorem A. if for every x, y ∈ R, there is a polynomial p(t) with integer coefficients, depending possibly on x and y, such that x - x2p(x), y] = 0, then R is commutative. In this paper, we define a property Fk of the polynomial f(x1,X2,…, xn) and prove, on the bassing is property, a theorem on the commutativity of rings. Herstein's theorem is just the one case when n = 1 in our theorem. |
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| Keywords: | Property Fk of polynomial Sum of coefficients of a polynomial Herstein theorem |
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