All-derivable points in the algebra of all upper triangular matrices Original Research Article

Let image be the algebra of all n×n upper triangular matrices. We say that an element image is an all-derivable point of image if every derivable linear mapping φ at G (i.e. φ(ST)=φ(S)T+Sφ(T) for any image with ST=G) is a derivation. In this paper we show that image is an all derivable point of image if and only if G≠0.