## Polynomial identities in ring theory (Google eBook)Polynomial identities in ring theory |

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### Contents

1 | |

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 |

Nonassociative PITheory | 327 |

Some Aspects of the History | 339 |

341 | |

Major Theorems Concerning Identities | 355 |

Major Counterexamples | 358 |

List of Principal notation | 359 |

361 | |

Pure and Applied Mathematics | 366 |

### Common terms and phrases

ACC(ideals Amitsur arbitrary assume automorphism Azumaya C-algebra canonical central extension central polynomial central simple Clearly commutative ring containing crossed product deﬁne Deﬁnition denote division algebra division ring domain elements equivalent Example Exercise F-algebra ﬁeld F ﬁnd ﬁnite dimensional ﬁrst Galois group given Hence homomorphic image idempotent implying induction inﬁnite injection integral involution irreducible isomorphism Jac(R Jacobson Kaplansky’s theorem left ideal Lemma Let F matrix maximal ideal maximal subﬁeld minimal left ideal module monomials mult-equivalent multilinear Nil(R nilpotent Noetherian nonzero notation PI-algebra PI-class PI-extension PI-ring PI-theory Pl-ring polynomial identity prime ideal primitive ring Procesi Proof proper maximally central prove QED Corollary QED Proposition QED Theorem QZ(R R-module rank rank(R rational identity Remark resp rings with involution Rowen satisﬁes semiprime semiprimitive soc(R spanned Spec(R subalgebra subdirect product submodule subring suitable Suppose T-ideal t-normal tensor product theory valuation ring write