MODULE AND GENERALIZED MODULE LEFT (m, n)-DERIVATIONS

Abstract

Fosner [3, 4] defined a module left (m, n)-derivation and a generalized module left (m, n)-derivation and proved the Hyers-Ulam stability of module left (m, n)-derivations and generalized module left (m, n)-derivations. In this note, we investigate the properties of module left (m, n)-derivation and generalized module left (m, n)-derivation. Furthermore, we prove that every module left (m, n)-derivation in C*-algebras is a zero mapping and that every generalized module left (m, n)-derivation in C*-algebras is a zero mapping.