Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we present some commutativity theorems for prime rings $R$ with involution $\ast$ of the second kind in which endomorphisms satisfy certain algebraic identities.
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Key Findings & Data:In this paper we present some commutativity theorems for prime rings $R$ with involution $\ast$ of the second kind in which endomorphisms satisfy certain algebraic identities.
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Conclusion & Impact:Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Prime ring · involution · commutativity
Abstract
In this paper we present some commutativity theorems for prime rings $R$ with involution $\ast$ of the second kind in which endomorphisms satisfy certain algebraic identities. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$
OUKHTITE, L., MIR, H. E., NEJJAR, B. (2020). ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION. International Electronic Journal of Algebra, Cilt: 28 - Sayı: 28, 127–140. https://ajindex.com/articles/832255
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