Abstract
We prove the Skolem–Noether Theorem for semiprime rings satisfying a strict identity: Let R be a centrally closed semiprime ring satisfying a strict identity. Suppose that σ is a C-linear automorphism of R. Then σ is X-inner and so is every C-linear σ-derivation of R.
ACKNOWLEDGMENTS
The authors are thankful to the referee for useful suggestions and comments. In particular, the referee suggested Beidar et al. (Citation1996, Lemmas 8.1.4 and 8.1.5) to simplify the proof of Proposition 2.2. This research was supported partly by the National Science Council of Taiwan.
Notes
†Member of Mathematics Division, National Center for Theoretical Sciences at Taipei.
Communicated by R. Wisbauer.