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Differential identities involving three generalized derivations on prime rings and Banach algebras

  • Karim Bouchannafa , Abderrahman Hermas EMAIL logo and Lahcen Oukhtite
Published/Copyright: March 28, 2025
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Abstract

Let L be a non-central Lie ideal of a prime ring R. The primary objective of this paper is to characterize generalized derivations β„‹ , β„± and 𝒒 of R satisfying the following algebraic identity:

x βŠ₯ β„‹ ⁒ ( y ) = β„± ⁒ ( x ) ⁒ y + y ⁒ 𝒒 ⁒ ( x )   for allΒ  ⁒ x , y ∈ L ,

where βŠ₯ represents either the Lie product [ β‹… , β‹… ] , or the Jordan product ∘ . Furthermore, we extend our results to Banach algebras.

References

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Received: 2024-07-18
Revised: 2024-12-23
Accepted: 2025-01-08
Published Online: 2025-03-28

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