Excursions in Ring Theory.

Format:

Book

Author/Creator:

Lam, T. Y.

Series:

Mathematics and Statistics Series

Language:

English

Physical Description:

1 online resource (731 pages)

Edition:

1st ed.

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.

Contents:

Intro

Preface

Table of Contents

Some Notations and Abbreviations

Chapter I Intrduction to Regular Rings

1. Regular Rings, Unit-Regular Rings, and IC Rings

Exercises for Section 1

2. Results on Regular Rings, and Finiteness Conditions

Exercises for Section 2

3. Strongly Regular Elements and Strongly Regular Rings

Exercises for Section 3

Chapter II Fitting Theory and Modules Over Regular Rings

4. Fitting Decomposition and Strong π-Regularity

Exercises for Section 4

5. Theorems on Strongly π-Regular Rings

Exercises for Section 5

6. Modules Over Regular Rings

Exercises for Section 6

Chapter III Generalized Inverses and Rings with Involutions

7. Drazin Inverses

Exercises for Section 7

8. Drazin Fibration

9. Moore-Penrose Inverses and-Rings

Exercises for Section 9

10. Drazin's (b,c)-Inverses, and Bott-Duffin Inverses

Exercises for Section 10

11. Rickart-Rings and-Regular Rings

Exercises for Section 11

Chapter IV Exchange Rings and Suitable Rings

12. Modules with the Exchange Property

Exercises for Section 12

13. Exchange Rings After Warfield

Exercises for Section 13

14. Suitable Rings After Nicholson

Exercises for Section 14

15.I0-Rings and Finiteness Conditions

Exercises for Section 15

16. PFA Condition, and Suitable Rings Versus Exchange Rings

Exercises for Section 16

Chapter V Clean Rings and Their Variations

17. Clean Rings and Nil-Clean Rings

Exercises for Section 17

18. Clean Rings Versus Suitable Rings

Exercises for Section 18

19. UCN Rings and UNC Rings

Exercises for Section 19

20. Strongly Clean Rings

Exercises for Section 20

21. USC Rings, SNC Rings, and UU Rings

Exercises for Section 21

22. Coping with the Identity Crisis

Exercises for Section 22.

Chapter VI Cancellation, Substitution, and Stable Range

23. Examples and Non-Examples of Cancellation

Exercises for Section 23

24. Introduction to Stable Range Theory

Exercises for Section 24

25. Cancellation, Substitution, and Perspectivity

Exercises for Section 25

26. B´ezout Rings and K-Hermite rings

Exercises for Section 26

References.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783032263018

OCLC:

1596870461