Characterization of Jordan two-sided centralizers and related maps on triangular rings. (English) Zbl 1529.16039
Summary: The main goal of this paper is to characterize Jordan two-sided centralizers, Jordan centralizers and related maps on triangular rings without identity. As an application of our main theorem, we characterize Jordan generalized derivations on triangular rings. Precisely, we prove that every Jordan generalized derivation on a triangular ring is a two-sided generalized derivation. As consequences, and apart from proving the other results, many known theorems can be either generalized or deduced.
MSC:
| 16W25 | Derivations, actions of Lie algebras |
| 47B47 | Commutators, derivations, elementary operators, etc. |
| 15A78 | Other algebras built from modules |
Keywords:
Jordan left (resp. right) centralizer; (Jordan) two-sided centralizer; (Jordan) two-sided generalized derivation; triangular ringReferences:
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