Introduction to Ring and Module Theory

著者名：Facchini, Alberto

Birkhäuser（2025/03/29発売）

• 言語：ENG
• ISBN：9783031825088
• eISBN：9783031825095

Description

This textbook is designed for a first course in ring theory, module theory and category theory. Written following several decades of teaching experience, it stands out with its clear and engaging style, featuring thorough explanations and attention to detail. Carefully selected exercises encourage active learning and problem-solving.

The textbook integrates elementary category theory with basic concepts and examples developed throughout the course. Although the primary focus is on rings and modules, relevant notions for other algebraic structures, such as groups and semigroups, are also discussed. Thus, this book aims at introducing students to noncommutative rings and modules within a broader algebraic context.

Aimed at advanced undergraduates or master students in mathematics, this textbook is suitable both for use in the classroom and self-study. Whereas the first part of the book covers a basic course in ring and module theory, the latter part includes optional deepening topics.

Table of Contents

- 1. Basic Notions.- 2. Some Classes of Modules.- 3. Right Artinian Rings.- 4. Local Rings, Injective Modules, Flat Modules.- 5. Additive Categories, Abelian Categories.- 6. Appendices.