Free Ideal Rings Local General Ring

Book Details:

• Author: Cohn

• Publisher: Cambridge University Press

• Edition: Illustrated

• Binding: Hardcover

• Number of Pages: 594

• ISBN: 9780521853378

• Release Date: 08-06-2006

• Languages: English

• Package Dimensions: 8.9 x 6.1 x 1.6 inches

About the Book:

"Free Ideal Rings" by Cohn provides an in-depth exploration of the theory of free ideal rings (FIRs), with a particular focus on rings exhibiting a weak algorithm. This book serves as an essential resource for advanced students and researchers in algebra, as it addresses complex mathematical concepts with clarity and precision.

Through detailed examples and exercises, Cohn delves into the generalization of the Euclidean algorithm, demonstrating how it applies to free associative algebras and rings where the variables do not commute. This leads to the understanding that all one-sided ideals in such rings are free, a fundamental result in algebra.

The book also covers the crucial topic of localization, offering a thorough treatment for general rings, while giving special emphasis to the features that arise in FIRs. Each chapter is supplemented with exercises, some of which present open problems, providing readers with the opportunity to engage deeply with the material.

In addition, historical notes at the end of each chapter give readers context and insight into the development of the theories and concepts discussed. Whether used as a textbook or as a reference for research, "Free Ideal Rings" provides a comprehensive foundation for anyone interested in the algebraic structures of rings and ideals.