Identities with generalized derivations in semiprime rings

Abstract: Let R be a semiprime ring. An additive mapping F: R → R is called a generalized derivation of R if there exists a derivation d: R → R such that F (xy) = F (x) y + xd (y) holds, for all x, y ∈ R. The objective of the present paper is to study the following situations: (1) [d (x), F (y)] = ±[x, y]; (2) [d (x), F (y)] = ±xοy; (3) [d (x), F (y)] = 0; (4) d (x)οF (y) = ±xοy; (5) d (x)οF (y) = ±[x, y]; (6) d (x)οF (y) = 0; (7) d (x) F (y)±xy ∈ Z (R), for all x, y in some appropriate subset of R.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Identities with generalized derivations in semiprime rings ; volume:46 ; number:3 ; year:2013 ; pages:453-460 ; extent:8 ; Demonstratio mathematica ; 46, Heft 3 (2013), 453-460 (gesamt 8)

Contributors, Places and Time

• Creator: Dhara, Basudeb ; Ali, Shakir ; Pattanayak, Atanu

Further information

• DOI: 10.1515/dema-2013-0471
• URN: urn:nbn:de:101:1-2411181441440.888932051240
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:20 AM CEST