Characterizing Jordan centralizers and Jordan generalized derivations on triangular rings through zero products

الأصل · EN

Let be a 2-torsion free triangular ring and let φ:→ be an additive map. We prove that if φ()+φ()=0 whenever,∈ are such that ==0, then φ is a centralizer. It is also shown that if τ:→ is an additive map satisfying t2 X,Y∈, XY=YX=0⇒ X τ(Y)+δ(X)Y+Yδ(X)+τ(Y)X=0, where δ:→ is an additive map satisfies X,Y∈, XY=YX=0⇒ X δ(Y)+δ(X)Y+Yδ(X)+δ(Y)X=0, then τ()=d()+ τ(1), where d:→ is a derivation and τ(1) lies in the centre of the. By applying this results we obtain some corollaries concerning (Jordan) centralizers and (Jordan) derivations on triangular rings.