Generalized Derivations and Derivations of Rings and Banach Algebras

Abstract

We investigate anti-centralizing and skew-centralizing mappings involving generalized derivations and derivations on prime and semiprime rings. We also obtain some range inclusion results for generalized linear derivations and linear derivations on Banach algebras by applying the algebraic techniques. Some results in this note are to improve the ones in [22].

What can be expected from a cubic derivation on finite dimensional algebras?

“…The image of derivations has a fairly long history. Results on the image of derivations defined on Banach algebras comprise a fruitful area of research intensively developed during the last sixty years (see [9,[13][14][15]17,24,25]). After considerations regarding this topic, no article was found to study the image of cubic derivations.…”