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.

Includes plenty of carefully chosen exercises Integrates elements of category theory Presents a modern and deep approach

Autorentext

Alberto Facchini studied at the University of Padua, getting the Laurea in Matematica magna cum laude in 1977. He has worked at the University of Udine from 1981 to 1999, becoming full professor of Algebra, and then at the University of Padua from 1999 to 2022. At present he is Emeritus Professor at the University of Padua. He also got fellowships to study and do research at the University of Sheffield, Universitat Autònoma de Barcelona, and Centre de Recerca Matemàtica. He has written about 180 scientific publications and has given lectures and talks at conferences in about forty different countries. In 1981 he received the Bonavera Prize in Mathematics.

He has been in the editorial boards of about fifteen mathematical journal, among which Bollettino dell'Unione Matematica Italiana, Communications in Algebra, Journal of Algebra and Its Applications, Rendiconti del Circolo Matematico di Palermo, and Rendiconti del Seminario Matematico dell'Università di Padova.

Inhalt

• 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.