Ring Theory

Ring Theory

Proceedings of a Conference on Ring Theory Held in Park City, Utah, March 2–6, 1971

1st Edition - January 1, 1972

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  • Editor: Robert Gordon
  • eBook ISBN: 9781483274157

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Description

Ring Theory provides information pertinent to the fundamental aspects of ring theory. This book covers a variety of topics related to ring theory, including restricted semi-primary rings, finite free resolutions, generalized rational identities, quotient rings, idealizer rings, identities of Azumaya algebras, endomorphism rings, and some remarks on rings with solvable units. Organized into 24 chapters, this book begins with an overview of the characterization of restricted semi-primary rings. This text then examines the case where K is a Hensel ring and A is a separable algebra. Other chapters consider establishing the basic properties of the four classes of projective modules, with emphasis on the finitely generated case. This book discusses as well the non-finitely generated cases and studies infinitely generated projective modules. The final chapter deals with abelian groups G that are injective when viewed as modules over their endomorphism rings E(G). This book is a valuable resource for mathematicians.

Table of Contents


  • Contributors

    Preface

    Restricted Semiprimary Rings

    Algebras with Hochschild Dimension ≤ 1

    Hereditarily and Cohereditarily Projective Modules

    Lifting Modules and a Theorem on Finite Free Resolutions

    On the Automorphism Scheme of a Purely Inseparable Field Extension

    Generalized Rational Identities

    K2 of Polynomial Rings and of Free Algebras

    Trivial Extensions of Abelian Categories and Applications to Rings: An Expository Account

    Higher K-Functors

    Properties of the Idealiser

    Structure and Classification of Hereditary Noetherian Prime Rings

    On the Representation of Modules by Sheaves of Modules of Quotients

    Some Remarks on Rings with Solvable Units

    Quasi-Simple Modules and Weak Transitivity

    Prime Right Ideals and Right Noetherian Rings

    Quotient Rings

    On the Identities of Azumaya Algebras

    Betti Numbers and Reflexive Modules

    Idealizer Rings

    Perfect Projectors and Perfect Injectors

    Linearly Compact Modules and Local Morita Duality

    Ideals in Finitely-Generated Pi-Algebras

    Introduction to Groups of Simple Algebras

    Modules over PIDs That Are Injective over Their Endomorphism Rings

    Problems

Product details

  • No. of pages: 396
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: January 1, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9781483274157

About the Editor

Robert Gordon

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