论文标题
三角形3矩阵环的乘法谎言推导
Multiplicative Lie derivation of triangular 3-matrix rings
论文作者
论文摘要
如果$ ϕ（[x，y]）= [ϕ（x），y]+[x，ϕ（y）] $在任何元素$ x，y $中保留$ [x，y]，其中$ [x，y] = xy-yx $是lie产品，则在关联环上的地图$ ϕ $称为多重谎言推导。在论文中，我们讨论了三角形3-matrix环上的乘法谎言衍生物$ \ MATHCAL T = {\ MATHCAL T} _3（\ MATHCAL R_I; \ MATHCAL M_ {IJ {IJ}）$。根据标准假设$ q_i \ Mathcal Z（\ Mathcal t）q_i = \ natcal z（q_i \ Mathcal t q_i）$，$ i = 1,2,3 $，我们表明，每个多重谎言衍生$φ中心有价值的地图消失了每个换向器。
A map $ϕ$ on an associative ring is called a multiplicative Lie derivation if $ϕ([x,y])=[ϕ(x),y]+[x,ϕ(y)]$ holds for any elements $x,y$, where $[x,y]=xy-yx$ is the Lie product. In the paper, we discuss the multiplicative Lie derivations on the triangular 3-matrix rings $\mathcal T={\mathcal T}_3(\mathcal R_i; \mathcal M_{ij})$. Under the standard assumption $Q_i\mathcal Z(\mathcal T)Q_i=\mathcal Z(Q_i\mathcal T Q_i)$, $i=1,2,3$, we show that every multiplicative Lie derivation $φ:\mathcal T\to\mathcal T$ has the standard form $φ=δ+γ$ with $δ$ a derivation and $γ$ a center valued map vanishing each commutator.
