On Lie-Type Derivations of Rings and Standard Operator Algebras by Local Actions

Let R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {R}}$$\end{document} be a unital prime ring with characteristic not 2 and containing a nontrivial idempotent p. In this article, we characterize the Lie-type derivation at zero product as well as idempotent product via certain assumptions. Further, we discuss the characterization of Lie-type derivations by local actions on some operator algebras.