设R是一个含单位元的可交换2无挠素环,且Mn(R)表示R上的n×n阶全矩阵代数。引入了保Jacobi恒等式的映射的概念,并对帆(R)(n≥4)上保Jacobi恒等式的线性映射的形式进行了考虑,得到了具体的刻画形式。
Let R be a 2-torsion-free commutative prime ring with a unity, and Mn (R)( n≥4) be the algebra consisting of all n× n matrices over R. First, the definition of maps preserving Jacobi identity was given, and then their properties were investigated. The main purpose of this paper is to present a concrete form of such kind of maps.