Introduction to Ring and Module Theory by Alberto Facchini ISBN 9783031825095, 9783031825088, 3031825098, 303182508X, B0F2SG23L7 instant download

Introduction to Ring and Module Theory by Alberto Facchini ISBN 9783031825095, 9783031825088, 3031825098, 303182508X, B0F2SG23L7 instant download

As far as prerequisites are concerned, in order to follow this textbook students must be familiar with the algebraic concepts studied in the first two years of a mathematics degree: linear algebra, basic group theory, principal integral domains, unique factorization domains, and Euclidean domains. Of course, additional knowledge in areas such as Galois theory, commutative algebra, algebraic geometry, or group theory will be advantageous. The selection of topics presented here stems from my personal views on what is essential for students at this stage (last year undergraduate students in mathematics and master students) relatively to their mathematical education. I believe the topics I have chosen are crucial for the students’ mathematical growth, their understanding of algebra’s foundational ideas, and their development of an algebraic mindset.

From author: Over the years, student interests have varied, prompting me to expand and adapt the material. While the full breadth of this textbook now exceeds what can be covered in a 60-hour course, this provides flexibility for lecturers to focus on specific areas. Numerous exercises are included to encourage active learning and problem-solving. The exercises proposed are fundamental in the learning of the topics presented.

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