Abstract
Let $\mathcal{A}$ be a unital algebra and $\mathcal{M}$ be a unital $\mathcal{A}$-bimodule. A characterization of generalized derivations and generalized Jordan derivations from $\mathcal{A}$ into $\mathcal{M}$, through zero products or zero Jordan products, is given. Suppose that $\mathcal{M}$ is a unital left $\mathcal{A}$-module. It is investigated when a linear mapping from $\mathcal{A}$ into $\mathcal{M}$ is a Jordan left derivation under certain conditions. It is also studied whether an algebra with a nontrivial idempotent is zero Jordan product determined, and Jordan homomorphisms, Lie homomorphisms and Lie derivations on zero Jordan product determined algebras are characterized.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.