半质环的交换性条件

傅昶林;郭元春

数学学报 ›› 1995, Vol. 38 ›› Issue (2)

数学学报 ›› 1995, Vol. 38 ›› Issue (2) DOI: 10.12386/A1995sxxb0027
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半质环的交换性条件

    傅昶林;郭元春
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Commutative Conditions for Semiprime Rings

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摘要

本文对满足可变恒等式的半质环在某种有界条件下给出了一个判断环R交换性的简便准则,使文献[2-27]中所有相应结果均成为其直接推论.此外,对不限有界的情况,也得到较为广泛的结论.

Abstract

Let R be a semiprime ring and C the center of R. In this paper following results areobtained:1.Suppose for any x_1,…,x_n∈R, there exists a polynomial f(t_1,…,t_n)(f dependingon x_1,…,x_n) such that f(x_1,…,x_n)∈C. If these polynomials satisfy the bounded condition,the sums of some coefficients of each f prime to each other, then R is commutative, which isageneralization of all related results in[ 2-27]. If f ls a polynomial, the sum of coefficients satisfiessome conditions, and for any x_1,…,x_n∈R, there exists an integer m(x_1,…,x_n)> 1 such thatf(x_1,…,x_n) ̄m(x_1,…,x_n)=f(x_1,…,x_n), then R is commutative.

关键词

可变恒等式 / 交换性 / 半质环

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傅昶林;郭元春. 半质环的交换性条件. 数学学报, 1995, 38(2) https://doi.org/10.12386/A1995sxxb0027
Commutative Conditions for Semiprime Rings. Acta Mathematica Sinica, Chinese Series, 1995, 38(2) https://doi.org/10.12386/A1995sxxb0027

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