University of Guilan Journal of Algebra and Related Topics 2345-3931 13 2 2025 12 01 Commutativity of prime rings involving multiplicative b-generalized derivation 165 176 8432 10.22124/jart.2025.26837.1635 EN W. Ahmed Department of Mathematics, Sreenidhi University, Hyderabad, India M. R. Mozumder Department of Mathematics, Aligarh Muslim University, Aligarh, India A. Abbasi School of Advanced Science and Languages, VIT Bhopal University, Madhya Pradesh, India H. M. Alnoghashi Department of Mathematics, Amran University, Amran, Yemen Journal Article 2024 02 23 ‎Let $\Qa_{mr}$ be a maximal right ring of quotients of $\Aa$‎, ‎where $\Aa$ is a prime ring‎. ‎A map $\Fa‎ : ‎\Aa \rightarrow \Qa_{mr}$ associated with derivation $d‎ : ‎\Aa \rightarrow \Aa$ is called a multiplicative $b$-generalized derivation (need not necessarily additive) if $\Fa(l m ) = \Fa(l )m‎ + ‎bl d(m )$ holds for all $l‎ ,‎m \in \Aa$ and for some $b \in \Qa_{mr}$‎. ‎In this article‎, ‎we study the commutativity of prime rings when the map $b$-generalized derivation satisfies the strong commutativity preserving condition and some central identities‎. https://jart.guilan.ac.ir/article_8432_bb7989e7ca919763886b5aa3d3515c5b.pdf