(θ1,θ2) - Derivation Pair on Rings | Ibn AL-Haitham Journal For Pure and Applied Sciences

Authors

Mohammed Khalid Shahoodh Ministry of Education, Ramadi Directorate of Education, Anbar-Iraq

DOI:

https://doi.org/10.30526/35.2.2723

Keywords:

ring theory, derivation theory, prime ring, derivation pair, semiprime ring

Abstract

Ring theory is one of the influential branches of abstract algebra. In this field, many algebraic problems have been considered by mathematical researchers who are working in this field. However, some new concepts have been created and developed to present some algebraic structures with their properties. Rings with derivations have been studied fifty years ago, especially the relationships between the derivations and the structure of a ring. By using the notatin of derivation, many results have been obtained in the literature with different types of derivations. In this paper, the concept of the derivation theory of a ring has been considered. This study presented the definition of

Ring theory is one of the influential branches of abstract algebra. In this field, many algebraic problems have been considered by mathematical researchers who are working in this field. However, some new concepts have been created and developed to present some algebraic structures with their properties. Rings with derivations have been studied fifty years ago, especially the relationships between the derivations and the structure of a ring. By using the notatin of derivation, many results have been obtained in the literature with different types of derivations. In this paper, the concept of the derivation theory of a ring has been considered. This study presented the definition of (θ1,θ2) derivation pair and Jordan (θ1,θ2)-derivation pair on an associative ring Γ, and the relation between them. Furthermore, we study the concept of prime rings under this notion by introducing some of its properties where θ1 and θ2 are two mappings of Γ into itself.

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