Abstract
In the present paper, it is shown that if a prime ring R admits a generalized derivation f associated with a nonzero derivation d such that either
or
then R is commutative. We apply this purely ring theoretic result to obtain commutativity of Banach algebras and prove that if A is a prime Banach algebra which admits a continuous linear generalized derivation f associated with a nonzero continuous linear derivation d such that either
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Articles in the same Issue
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Articles in the same Issue
- Frontmatter
- On a Caputo-type fractional derivative
- Well-posedness, blow-up dynamics and controllability of the classical chemotaxis model
- Sine and cosine type functional equations on hypergroups
- Solvability of positive solutions for a systems of nonlinear fractional order BVPs with p-Laplacian
- On commutativity of rings and Banach algebras with generalized derivations
- Extension of Zelazko’s theorem to n-Jordan homomorphisms
- Asymptotic behavior of the Timoshenko-type system with nonlinear boundary control