Products of generalized derivations on rings

S. R. Behresi; M. J. Mehdipour

paper

Products of generalized derivations on rings

arXiv:2301.09139

Abstract

In this paper, we show that if the product $(D_{1} D_{2}, d_{1} d_{2})$ of generalized derivations $(D_{1}, d_{1})$ and $(D_{2}, d_{2})$ on an algebra $A$ is a generalized derivation, then $d_{1} D_{2}$ and $d_{2} D_{1}$ map $A$ into $rad (A)$ . Also, for generalized derivations $(D_{1}, d_{1})$ and $(D_{2}, d_{2})$ on a prime ring with characteristic different from two, we give necessary and sufficient conditions under which $(D_{1}^{2} + D_{1} D_{2}, d_{1}^{2} + d_{1} d_{2})$ is a generalized derivation as well.