Aron Simis Libri

Focusing on commutative algebra, the book is designed for readers with a foundational understanding of algebraic structures, without requiring extensive knowledge of group or field theory. It introduces modern concepts and methods, featuring a "Discussion" section after each chapter to connect previous and new ideas. Emphasizing the computational aspects of the theory, it highlights the importance of algorithms in mathematics. The content is derived from lectures at the Mathematics Department of UFPE, aiming to engage novices with the practical applications of definitions and theorems.

The primary audience for this book is students and young researchers interested in the core of commutative algebra, a self-contained discipline that can be quite dry for beginners with only basic training in algebra and calculus. This stable mathematical field encompasses essential topics that are universally accepted and practiced. Authors often condense these topics into a short list of fundamental facts, but there is a delicate balance between elegance and usefulness, especially for novices. From my teaching experience, I have found that elegance and terseness are not effective for beginners; instead, the material must be rich in motivation, justification, and practical pointers. To address this, I have divided the content into three parts: starting with elementary sections, transitioning through more challenging themes for a smooth progression, and concluding with advanced topics reflecting current trends in commutative algebra. Each chapter includes historical notes that offer insights into original sources and background information on specific subjects or theorems. Additionally, exercises are provided to encourage practical application of the theory to solve concrete problems, including those involving actual polynomials.