“Exercises in Classical Ring Theory” by T.Y Lam is a comprehensive textbook that provides students with a deep understanding of ring theory and its applications. This book is widely used by students and teachers alike, due to its clear explanations, numerous exercises, and well-structured format.
The textbook covers all the essential topics in classical ring theory, including basic algebraic structures, ideals, modules, and more advanced concepts such as Noetherian rings, Artinian rings, and local rings. Lam’s writing style is clear and concise, making it easy for students to grasp the material and apply it to real-world problems.
In addition to its well-written explanations, the “Exercises in Classical Ring Theory” also features a large number of exercises and problems that test the student’s understanding of the material. This makes it an ideal resource for both self-study and classroom use. The exercises are carefully chosen to reinforce the concepts introduced in each chapter and to provide students with a deeper understanding of the material.
TABLE OF CONTENTS
Wedderburn-Artin Theory
- Basic Terminology and Examples
- Semisimplicity
- Structure of Semisimple Rings
Jacobson Radical Theory
- The Jacobson Radical
- Jacobson Radical Under Change of Rings
- Group Rings and the J-Semisimplicity Problem
Introduction to Representation Theory
- Modules over Finite-Dimensional Algebras
- Representations of Groups
- Linear Groups
Prime and Primitive Rings
- The Prime Radical; Prime and Semiprime Rings
- Structure of Primitive Rings; the Density Theorem
- Subdirect Products and Commutativity Theorems
Introduction to Division Rings
- Division Rings.
- Some Classical Constructions
- Tensor Products and Maximal Subfields
- Polynomials over Division Rings
Ordered Structures in Rings
- Orderings and Preordering in Rings
- Ordered Division Rings
Local Rings, Semilocal Rings, and Idempotents
- Local Rings
- Semilocal Rings
- The Theory of Idempotents
- Central Idempotents and Block Decompositions
Perfect and Semiperfect Rings
- Perfect and Semiperfect Rings
- Homological Characterizations of Perfect and Semiperfect
- Rings
- Principal Indecomposables and Basic Rings
We are happy to announce that this valuable textbook is available in PDF format for students to download and study from. This is especially useful for students who are looking for a convenient and accessible way to study ring theory, as well as for teachers who want to make sure their students have access to the material they need.
In conclusion, “Exercises in Classical Ring Theory” by T.Y Lam is a must-have resource for anyone looking to deepen their understanding of ring theory. With its clear explanations, numerous exercises, and well-structured format, students will find this book an invaluable tool in their journey to mastering this fascinating subject. So, if you’re looking to further your understanding of ring theory, be sure to download the PDF version of “Exercises in Classical Ring Theory” today.
