University of Guilan Journal of Algebra and Related Topics 2345-3931 10 1 2022 06 01 A note on generalized derivations on prime ideals 159 169 5623 10.22124/jart.2021.20131.1291 EN N. Rehman Department of Mathematics Aligarh Muslim University Aligarh, India H. M. Alnoghashi Department of Mathematics Aligarh Muslim University Aligarh, India M. Hongan Department of Mathematics, Seki 772, Maniwa, Okayama, Japan. Journal Article 2021 07 12 This paper investigates the structure of the quotient ring $\mathscr{R}/ \mathscr{P}$, where $\mathscr{R}$ is an arbitrary ring and $\mathscr{P}$ is a prime ideal of $\mathscr{R}$ . We show that the structure of this class of rings has a relationship with the behaviour of generalized derivations satisfying algebraic identities involving prime ideals. https://jart.guilan.ac.ir/article_5623_4b2731c22ceb4a0ffddd7b40329ac424.pdf