Commutativity of prime rings involving multiplicative b-generalized derivation

Document Type : Research Paper

Authors

1 Department of Mathematics, Sreenidhi University, Hyderabad, India

2 School of Advanced Science and Languages, VIT Bhopal University, Madhya Pradesh, India

3 Department of Mathematics, Amran University, Amran, Yemen

Abstract

‎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.

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References

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Journal of Algebra and Related Topics
Volume 13, Issue 2
December 2025
Pages 165-176

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