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On generalized derivations involving prime ideals

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Abstract

In this paper, we use generalized derivations to investigate the behaviour of prime ideal satisfying contain function identities. In certain cases, the structure of the quotient ring \({\mathscr {R}}/{\mathscr {P}}\) will be determined, where \({\mathscr {R}}\) is an arbitrary ring and \({\mathscr {P}}\) is a prime ideal of \({\mathscr {R}}\).

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Acknowledgements

The authors are greatly indebted to the referee for his/her valuable suggestions, which have immensely improved the paper. For the first author, this research is supported by the Council of Scientific and Industrial Research (CSIR-HRDG), India, Grant No. 25(0306)/20/EMR-II.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Nadeem ur Rehman & Hafedh M. Alnoghashi

  2. Maniwa, Japan

    Motoshi Hongan

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  1. Nadeem ur Rehman
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  2. Motoshi Hongan
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  3. Hafedh M. Alnoghashi
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Correspondence to Nadeem ur Rehman.

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Rehman, N.u., Hongan, M. & Alnoghashi, H.M. On generalized derivations involving prime ideals. Rend. Circ. Mat. Palermo, II. Ser 71, 601–609 (2022). https://doi.org/10.1007/s12215-021-00639-1

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  • DOI: https://doi.org/10.1007/s12215-021-00639-1

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