Abstract
Our goal in the present paper is to study a connection between the commutativity of rings and the behaviour of its generalized derivations. More specifically, we investigate commutativity of quotient rings R/P where R is any ring and P is a prime ideal of R which admits generalized derivations satisfying certain algebraic identities acting on prime ideal P without the primeness (semi-primeness) assumption on the considered ring. This approach allows us to generalize some well known results characterizing commutativity of rings.
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24 December 2020
A Correction to this paper has been published: https://doi.org/10.1007/s12215-020-00583-6
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The original version of this article was revised: The article was published in SpringerLink with open access. With the author(to step back from Open Choice, the copyright of the article changed on December 2020 to © Springer-Verlag Italia S.r.l., part of Springer Nature 2020.
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Abdellah, M., Lahcen, O. & Mohammed, Z. Prime ideals and generalized derivations with central values on rings. Rend. Circ. Mat. Palermo, II. Ser 70, 1633–1643 (2021). https://doi.org/10.1007/s12215-020-00578-3
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DOI: https://doi.org/10.1007/s12215-020-00578-3