摘要
设Ｚ（Ｒ）为环Ｒ的中心。本文证明了满足下列条件之一的环Ｒ是交换环：（Ａ１）Ｒ是半素环，且对任意ａ１，ａ２，…，ａｎ∈Ｒ，存在整系数多项式ｆ（ｘ１，ｘ２，…，ｘｎ）及ｎ元置换σ，使得ａ１ａ２…ａｎ－ａσ（１）ａσ（２）…ａσ（ｎ）ａ１ｆ（ａ１，ａ２，…，ａｎ）∈Ｚ（Ｒ）；（Ｂ１）对任意ａ１，ａ２∈Ｒ，存在整系数多项式ｆ（ｘ１，ｘ２）及２元置换σ，使得ａ１ａ２＝ａσ（１）ａσ（２）ａ１ｆ（ａ１，ａ２）。
Let R be a ring,Z(R) be the centre of R.This paper proves that R is commutative if R satisfies one of the following conditions:(A1) R is a semiprime ring,and for all a1,a2…,an in R,there exists a polynomial f(x1,x2…,xn) with integer coefficients and an n-permutation σ such that a1a2…an-aσ(1)aσ(2)…aσ(n)a1f(a1,a2,…,an) ∈Z(R);(B1) for all a1,a2 in R,there exists a polynomial f(x1,x2) with integer coefficients and a 2- permutation σ such that a1a2=aσ(1)aσ(2)a1f(a1,a2).
出处
《福建师范大学学报（自然科学版）》
CAS
CSCD
1994年第1期10-13,共4页
Journal of Fujian Normal University：Natural Science Edition
关键词
半单纯环
交换环
交换性定理
semiprime ring,J-semisimple ring,subdirect sum
