University of Guilan Journal of Algebra and Related Topics 2345-3931 12 1 2024 07 01 A note on generalized derivations and left ideals of prime rings 89 103 7861 10.22124/jart.2023.23820.1502 EN G. S. Sandhu Department of Mathematics, Patel Memorial National College, Rajpura, India A. Boua Department of Mathematics, Physics and Computer Science, Sidi Mohammed Ben Abdellah University, Taza, Morocco Journal Article 2023 02 09 Let $R$ be a prime ring and $Z(R)$ denotes the center of $R$. In this study, we expose the commutativity of $R$ as a consequence of specific differential identities involving derivations acting on left ideals of $R$. Finally, we give examples that demonstrate the necessity of hypotheses taken in the theorems. prime ring left ideal Derivation generalized derivation https://jart.guilan.ac.ir/article_7861_c2f8ce27be8421baf6c75096c46f3ddc.pdf