On Local (like) Derivations on Path Algebras

Abstract

In this paper, we investigate local derivations and local generalized derivations on path algebras associated with finite acyclic quivers. We show that every local derivation on a path algebra is a derivation, and every local generalized derivation on a path algebra is a generalized derivation. Also, we apply main results on several related maps to local derivations. The established results generalize several ones on some known algebras such as incidence algebras.