In this paper, the author gives a description of the derivations of $UT{M}_n(R)$, the ring of upper triangular matrices over an associative ring R with identity. The main result states that if D is an arbitrary derivation of the ring $UT{M}_n(R)$ and $A\in UT{M}_n(R)$, then there are matrices, such that the derivative $D(A)$ is a linear combination of the values of well-known derivations of these matrices.

中文翻译：

---

三角矩阵环的推导

在这篇论文中，作者给出了推导的描述$ü吨{米}_n(R)$，上三角矩阵环在具有恒等性的结合环R上。主要结果表明如果D是环的任意推导$ü吨{米}_n(R)$和$A\in ü吨{米}_n(R)$, 然后有矩阵, 这样导数$丁(A)$是这些矩阵的众所周知的推导值的线性组合。