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Commutativity criteria of prime rings involving two endomorphisms
Souad Dakir,Abdellah Mamouni,Mohammed Tamekkante 대한수학회 2022 대한수학회논문집 Vol.37 No.3
This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.
Generalized derivations in ring with involution involving symmetric and skew symmetric elements
Souad Dakir,Hajar El Mir,Abdellah Mamouni 대한수학회 2024 대한수학회논문집 Vol.39 No.1
In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.