Study of the structure of quotient rings satisfying algeraic identities

Document Type : Research Paper

Authors

1 Department of Mathematics, Polydisciplinary Faculty, Taza Sidi Mohamed Ben Abdellah University, Fes Morocco

2 Department of Mathematics, Polydisciplinary Faculty, Taza Sidi Mohamed Ben Abdellah University, Fes, Morocco

Abstract

‎Assuming that $\mathcal{R}$ is an associative ring with prime ideal $P$‎, ‎this paper investigates the commutativity of the quotient ring $\mathcal{R}/P$‎, ‎as well as the possible forms of generalized derivations satisfying certain algebraic identities on $\mathcal{R}.$ We give results on strong commutativity‎, ‎preserving generalized derivations of prime rings‎, ‎using our theorems‎. ‎Finally‎, ‎an example is given to show that the restrictions on the ideal $P$ are not superfluous.‎

Keywords

Journal of Algebra and Related Topics
Volume 11, Issue 2
December 2023
Pages 117-125

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