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Structure of a quotient ring \(\pmb {R/P}\) with generalized derivations acting on the prime ideal P and some applications

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Abstract

The main purpose of this paper is to develop a new approach that consists to investigate the structure of a quotient ring R/P via action of generalized derivations on the prime ideal P. In this direction, we initiate new classes of additive mappings extending both of centralizing and commuting mappings. Furthermore, for an arbitrary ring, we will consider algebraic identities based on its prime ideals. As an application, we obtain some results concerning invariance of minimal prime ideals of a semiprime ring under derivations.

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Author notes

  1. These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics and informatics, Polydisciplinary Faculty, Sultan Moulay Slimane University, Box 592, Beni Mellal, Morocco

    Moulay Abdallah Idrissi

  2. Laboratory of Modeling and Mathematical Structures, Department of Mathematics, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University, Box 2202, Fez, Morocco

    Lahcen Oukhtite

Authors
  1. Moulay Abdallah Idrissi
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  2. Lahcen Oukhtite
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Correspondence to Moulay Abdallah Idrissi.

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Communicated by B. Sury.

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Idrissi, M.A., Oukhtite, L. Structure of a quotient ring \(\pmb {R/P}\) with generalized derivations acting on the prime ideal P and some applications. Indian J Pure Appl Math 53, 792–800 (2022). https://doi.org/10.1007/s13226-021-00173-x

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  • DOI: https://doi.org/10.1007/s13226-021-00173-x

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