Generalized Derivations in Rings and Their Applications to Banach Algebra

Alali A. S., Sögütcü E. K., BEDİR Z., Rehman N. u.

Mathematics, cilt.14, sa.2, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3390/math14020295
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: Banach algebras, derivation, generalized derivation, ideal, prime ring, semiprime ring
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

Let (Formula presented.) be a prime ring, and let F denote a generalized derivation associated with a derivation d of (Formula presented.). Consider I as a nonzero ideal of (Formula presented.), and let (Formula presented.) 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 (Formula presented.), (Formula presented.) 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.