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Abstract
Let be a non-commutative prime ring with
its maximal right ring of quotients. It is proved that the functional identity
for bi-additive maps
only has the trivial solution. Basing on the result, we characterize Jordan
-derivations and generalized Jordan semiderivations in terms of derivations,
-derivations and semiderivations.
Acknowledgement
The author is grateful to the referee for carefully reading the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Funding
The work was supported in part by the Ministry of Science and Technology of Taiwan MOST [grant number 103-2115-M-002-004-MY2]; and the National Center for Theoretical Sciences, Taipei Office.