Automorphism groups of certain algebras of triangular matrices (Q689647)

Let \(R\) be a ring with unity and let \(T_ n(R)\) be the ring of upper triangular \(n\times n\) matrices over \(R\). When \(R\) is an indecomposable semiprime ring, we give a full description of the automorphism group of \(T_ n(R)\). This group is shown to be the semidirect product of a normal subgroup consisting of certain inner automorphisms by the subgroup of the automorphisms induced by automorphisms of \(R\). We also show that every \(R\)-automorphism of \(T_ n(R)\) is inner, for an arbitrary ring \(R\) (with unity).