Derivations of upper triangular matrix rings
Let \(R\) be a ring with unity. The authors consider derivations of the ring \(T_ n(R)\), the ring of \(n\times n\) upper triangular matrices over \(R\). For a derivation \(d\) of \(R\), \(\overline{d}\) denotes the derivation that is induced by \(d\) on \(T_ n(R)\). For a matrix \(A\) in \(T_ n(R)\), \(d_ A\) is the inner derivation induced by \(A\). The main result of the paper is that every derivation of \(T_ n(R)\) is of the form \(\overline{d}+d_ A\), where \(d\) is a derivation of \(R\) and \(A\) is in \(T_ n(R)\).
scientific article; zbMATH DE number 399304