Ring Theory

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.

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