## Polynomial Identities in Ring TheoryPolynomial Identities in Ring Theory |

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### Contents

Chapter 2 The General Theory of Identities and Related Theories | 109 |

Chapter 3 Central Simple Algebras | 151 |

Chapter 4 Extensions of PIRings | 202 |

Chapter 5 Noetherian PIRings | 224 |

Chapter 6 The Theory of the Free Ring Applied to Polynomial Identities | 239 |

Chapter 7 The Theory of Generalized Identities | 254 |

Chapter 8 Rational Identities Generalized Rational Identities and Their Applications | 289 |

Central Polynomials of Formanek | 315 |

Nonassociative PITheory | 327 |

Some Aspects of the History | 339 |

341 | |

Major Theorems Concerning Identities | 355 |

Major Counterexamples | 358 |

359 | |

361 | |

Pure and Applied Mathematics | 366 |

### Common terms and phrases

Amitsur arbitrary assume automorphism Azumaya canonical central extension central polynomial central simple coefficients commutative ring crossed product define Definition deg(f denote division algebra division ring domain elements equivalent Example Exercise F-algebra field F field of fractions finite dimensional finite number Galois group given Hence homomorphic image idempotent identity of degree implying induction infinite injection integral involution irreducible isomorphism Jac(R Jacobson Kaplansky's theorem left ideal Lemma Let F matric units maximal ideal maximal subfield minimal left ideal module monomials mult-equivalent multilinear Nil(R nilpotent nonzero notation PI-algebra PI-class PI-extension PI-theory polynomial identity prime ideals prime PI-ring primitive ring Proof prove QED Corollary QED Proposition QED Theorem R-module rank rank(R rational identity Remark resp rings with involution Rowen semiprimitive soc(R Spec(R subalgebra subdirect product submodule subring suitable Suppose T-ideal t-normal tensor product theory valuation ring write