SCIENCE ASIA

Volume 46, No. 06, Month DECEMBER, Year 2020, Pages 738 - 745

Multiplicative jordan derivations on triangular n-matrix rings

Huimin Chen, Xiaofei Qi

Abstract Download PDF

Let T be a triangular n-matrix ring (n ? 2) and ? : T ! T a map. It is shown that ? is a multiplicative Jordan derivation if and only if one of the statements holds: (1) if T is 2-torsion free, then ? is an additive derivation; (2) if T is 2-torsion, under some mild assumptions, then ?(X ) = d(X ) + ?(X ) holds for all X 2 T , where d : T ! T is an additive derivation and ? is a map from T into its center vanishing on all elements X Y + Y X for X, Y 2 T . This generalizes some related known results.

Keywords

Jordan derivations, derivations, triangular rings, triangular n-matrix rings

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