Centralizers satisfying polynomial identities |
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Authors: | Susan Montgomery |
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Institution: | (1) Department of Mathematics, University of Southern California, 90007 Los Angeles, California, U. S. A. |
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Abstract: | The following results are proved: IfR is a simple ring with unit, and for someaεR witha
n in the center ofR, anyn, such that the centralizer ofa inR satisfies a polynomial identity of degreem, thenR satisfies the standard identity of degreenm. WhenR is not simple,R will satisfy a power of the same standard identity, provided thata andn are invertible inR. These theorems are then applied to show that ifG is a finite solvable group of automorphisms of a ringR, and the fixed points ofG inR satisfy a polynomial identity, thenR satisfies a polynomial identity, providedR has characteristic 0 or characteristicp wherep✗|G|.
This research was supported in part by NSF Grant No. GP 29119X. |
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