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The main purpose of this paper is to show that every Jordan centralizer andevery Jordan two-sided centralizer is a centralizer on triangular rings withoutassuming unity. As an application, we prove that every Jordan generalizedderivation on a triangular ring is a two-sided generalized derivation. Someother related results are also discussed.

Characterization of Jordan centralizers and Jordan two-sided centralizers on triangular rings without assuming unity