## Fixed Rings of Finite Automorphism Groups of Associative Rings |

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### Contents

Preliminaries | 1 |

inner and outer automorphisms simple | 19 |

Inner and outer automorphisms of semiprime rings | 38 |

Copyright | |

5 other sections not shown

### Common terms and phrases

assume that G Chapter claim completely outer contradiction Corollary l.5 coset define denote direct sum division ring domain e.Re Example finite direct sum finite group finite R module finitely-generated fixed elements follows G acts g e Aut(R g e G G is X-outer G-lattice polynomials G|-torsion Goldie ring group algebra group G group of automorphisms homomorphism ideal of R*G idempotent inner automorphisms J(RG Kharchenko left ideal Let G let H Maschke's theorem nilpotent elements Noetherian non-degenerate non-trivial partial trace non-zero ideal normal subgroup Osterburg p-group p-torsion partial trace functions Passman PI of degree polynomial identity prime ring Proposition proved quotient ring R-module R*G is semiprime result satisfies a PI semi-simple Artinian semiprime ideals simple Artinian simple rings skew group ring sum of simple summand tG(R Theorem l.4 trace functions exist unit element Z(RG