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Abstract
Let R be a semiprime ring with Q ml (R) the maximal left ring of quotients of R. Suppose that T: R → Q ml (R) is an additive map satisfying T(x 2) = xT(x) for all x ∈ R. Then T is a right centralizer; that is, there exists a ∈ Q ml (R) such that T(x) = xa for all x ∈ R.
ACKNOWLEDGMENTS
The authors are grateful to the referee for carefully reading their manuscript. The valuable suggestions have simplified the paper greatly. The work of T.-K. Lee was supported by NSC of Taiwan and NCTS/Taipei, and that of T.-L. Wong by NSC of Taiwan.
Notes
Communicated by M. Bresar.
b Member of Mathematics Division, NCTS (Taipei Office).