A Course in Ring Theory (AMS Chelsea Publishing)

Book Details

• Publisher: Chelsea Pub Co

• Author: Passman, Donald S.

• Language: English

• Binding: Hardcover

• ISBN: 9780821836804

• Release Date: 01-05-2005

• Package Dimensions: 10.2 x 7.3 x 0.9 inches

About The Book

First published in 1991, this book provides the core material for an undergraduate first course in ring theory, with a focus on projective and injective modules. Donald S. Passman brings a comprehensive approach to both commutative and noncommutative ring theory, covering various essential aspects of the field.

The book is divided into three parts:

• Part I: Projective Modules
  It starts with the basics of module theory and progresses into an in-depth study of special classes of rings such as Wedderburn, Artinian, Noetherian, hereditary rings, and Dedekind domains. The section concludes with an introduction to projective dimension.

• Part II: Polynomial Rings
  This part explores polynomial rings in a noncommutative setting, providing significant results like the Hilbert Syzygy Theorem and Hilbert Nullstellensatz.

• Part III: Injective Modules
  It covers topics such as the Goldie Theorems and characterizations of injective modules over Noetherian rings.

This book is ideal for graduate students and researchers with a keen interest in ring theory. It also includes exercises and a list of additional reading for further exploration.

Key Features

• Comprehensive coverage of ring theory, projective and injective modules

• Numerous exercises to reinforce understanding

• Additional reading suggestions for deeper knowledge

• ISBN: 9780821836804

• Package Dimensions: 10.2 x 7.3 x 0.9 inches