## Ring Theory, 83: Student EditionThis is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS |

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### Contents

1 | |

21 | |

Chapter 2 Basic Structure Theory | 119 |

Chapter 3 Rings of Fractions and Embedding Theorems | 271 |

Chapter 4 Categorical Aspects of Module Theory | 357 |

Chapter 5 Homology and Cohomology | 369 |

Chapter 6 Rings with Polynomial Identities and Affine Algebras | 435 |

Chapter 7 Central Simple Algebras | 497 |

Chapter 8 Rings from Representation Theory | 519 |

Dimensions for Modules and Rings | 583 |

Major Ring and ModuleTheoretic Results Proved in Volume I Theorems and Counterexamples also cf Characterizations | 585 |

Major Theorems and Counterexamples for Volume II | 593 |

The Basic RingTheoretic Notions and Their Characterizations | 603 |

References | 607 |

615 | |

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### Common terms and phrases

abelian affine Artinian ring assume automorphism bimodule C-algebra canonical central simple chain composition series contains cyclic define Definition denote dimension direct sum division algebra division ring domain element epic equivalent exact sequence example exercise extension F-algebra field F finite dimensional functor given GK dim Goldie Hence Hint homomorphic image idempotent implying induction injective invertible isomorphism Jac(R Jacobson K-dim ker f left Artinian left ideal left Noetherian lemma Lie algebra map f maximal ideal minimal left ideal monic monoid morphism multiplication Nil(R nilpotent Noetherian ring nonzero Note Nullstellensatz PI-ring prime ideals primitive ring projective module projective resolution Proof prove Q.E.D. Corollary Q.E.D. Proposition quasi-invertible R-module regular Remark result ring of fractions ring theory satisfies semiperfect semiprime semisimple Artinian simple Artinian simple module Spec(R subalgebra subgroup submodule subring suitable summand Suppose write