Work

Generalized Derivations in Rings and Their Applications to Banach Algebra

Year: 2026

Type: article

Abstract: Let R be a prime ring, and let F denote a generalized derivation associated with a derivation d of R. Consider I as a nonzero ideal of R, and let m,n,k,l be fixed positive integers. In this study, we explore the behavior of the generalized derivation F within the structures of both prime and semiprime rings that satisfy the functional identity [F(η),d(τ)]m=ηn[η,τ]lηk, ∀,η,τ∈I. Furthermore, we extend this investigation to the framework of Banach algebras, analyzing how generalized derivations operate in such algebras. A comparative discussion is also presented to highlight the distinctions and similarities in the behavior of generalized derivations within Banach algebraic settings under the above structural condition.

Source: Mathematics

DOI: 10.3390/math14020295

Authors: Amal S. Alali, Emine Koç Sögütcü, Zeliha Bedir, Nadeem ur Rehman

Institutions: Princess Nourah bint Abdulrahman University, Kilis 7 Aralık University, Sivas Cumhuriyet Üniversitesi, Aligarh Muslim University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Princess Nourah Bint Abdulrahman University