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

Moulay Abdallah Idrissi () and Lahcen Oukhtite ()
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Moulay Abdallah Idrissi: Sultan Moulay Slimane University
Lahcen Oukhtite: Sidi Mohamed Ben Abdellah University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 3, 792-800

Abstract: 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.

Keywords: Prime ideal; Generalized derivations; Quotient ring; Commutativity; 16U80; 16D25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00173-x

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