Excursions in ring theory T. Y. Lam

Format:

Book

Author/Creator:

Lam, T. Y. (Tsit-Yuen), 1942- author.

Series:

Oregon State monographs. Mathematics and statistics series

Mathematics and Statistics Series

Language:

English

Subjects (All):

Rings (Algebra).

Physical Description:

1 online resource

Place of Publication:

Cham Springer 2026

Summary:

This self-contained graduate text provides a readily available source of information and reference for a substantial part of ring theory developed over the last 80 years. The book completes a trilogy with the author's A First Course in Noncommutative Rings and Lectures on Modules and Rings. It deals with a number of current topics in noncommutative algebra, ranging from von Neumann regular rings, unit-regular rings and strongly regular rings, exchange (or "suitable") rings, to clean, strongly clean, and nil-clean rings, with a dosage of the popular theory of generalized inverses (including Drazin inverses and Moore-Penrose inverses) in between. Following all of the above ring-theoretic "excursions", the text concludes with a final chapter on the issues of cancellation and substitution of modules, along with a discussion on the relatively classical stable range theory of rings. The rich exercise sets for the various chapters of the book are designed to be especially helpful for students and researchers alike who desire to deepen their understanding of noncommutative algebra

Contents:

Chapter 1. Introduction to Regular Rings

Chapter 2. Fitting Theory and Modules Over Regular Rings

Chapter 3. Generalized Inverses and Rings with Involutions

Chapter 4. Exchange Rings and Suitable Rings

Chapter 5. Clean Rings and their Variations

Chapter 6. Cancellation, Substitution, and Stable Range

Notes:

Online resource; title from PDF title page (SpringerLink, viewed July 6, 2026)

ISBN:

9783032263018

3032263018

OCLC:

1602311581

Access Restriction:

Restricted for use by site license