Right Centralizers of Semiprime Rings

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.

Key Words:

• Extended centroid
• Functional identity
• Orthogonal completion
• PI-ring
• Prime ring
• Semiprime ring

2010 Mathematics Subject Classification:

• 16N60
• 16W10
• 16R60

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).