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Abstract
Let be a unital prime ring with characteristic not 2 and containing a nontrivial idempotent. Assume that
is a surjective map. It is shown that f is strong 3-commutativity preserving, that is, f satisfies
for all
, if and only if
for all
, where
is an element in the extended centroid of
with
and
is a map from
into its extended centroid. Applications to prime C
-algebras, factor von Neumann algebras, standard operator algebras and matrix algebras are also obtained .
Acknowledgements
The authors wish to give their thanks to the referees for their helpful comments.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work is partially supported by Natural Science Foundation of China [grant number 11671006], [grant number 11671294]; Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi.