结合环的约当微商

来源期刊：中南大学学报(自然科学版)1991年第6期

论文作者：殷志云

文章页码：98 - 101

关键词：约当微商; 正则元; T理想

Key words：Jordan derivation; regular element; T ideal

摘    要：设R是一个结合环,满足由2x=0,x∈R,可推出x=0,N是R的一个非零理,D₁,D₂是R的二个约当微商,使D₁(N)和D₂(N)分别含有R的一个交换子正则元,且对任意a,b∈N,都有D₁(a)D₂(b)=D₂(b)D₁(a),则R是交换环。

Abstract: In this paper the following results are proved: 1. Let R be an associative ring in which 2x=0 implies x=0, and N bean (nonzero) ideal of R and D₁, D₂ be two Jordan derivations on R, such thatD₁(N) and D₂(N) contain a regular element of R respectively. If R satisfies D₁ (α)D₂ (b)=D₂ (b)D₁ (α)for all α, b∈N, then R is commutative. 2. Let R be an associative ring and D be a nonzero mapping of R suchthat D (α+b) =D (α)+ D (b) and D (αb) = D (b)α+ bD (α)If any T ideal(≠0) of R contains a regular element in R, the R is commu-tative.