Derivations of upper triangular matrix rings
type: Item
instance of: scholarly article
title: Derivations of upper triangular matrix rings
zbMATH Open document ID: 0781.16020
DOI: 10.1016/0024-3795(93)90141-A
author: Sônia P. Coelho
author: C. Polcino Milies
published in: Linear Algebra and its Applications
publication date: 1993-08-29T00:00:00Z
review text: 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 \(T_ n(R)\).
reviewed by: Søren Jøndrup
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 399304
zbMATH Keywords: ring of upper triangular matrices
zbMATH Keywords: derivations
zbMATH Keywords: inner derivation
MaRDI profile type: Publication
cites work: Automorphism groups of algebras of triangular matrices
cites work: Automorphisms of algebras of upper triangular matrices
cites work: Derivations with Invertible Values
cites work: Derivations and Automorphisms of Nonassociative Matrix Algebras
cites work: Automorphisms of upper triangular matrix rings
cites work: Diffrential polynomial rings and morita equivalence
full work available at URL: 0024-3795(93)90141-a
OpenAlex ID: W1963481615
description: scientific article; zbMATH DE number 399304