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Numerical Semigroups
A Commutative Algebra Approach
Introduction
This book offers an exploration of the rich interplay between numerical semigroups and commutative algebra. It fills a notable gap in the literature by bridging numerical semigroup theory with advanced algebraic methods.
Structure
The book is structured to support both self-study and advanced coursework, and it is divided into two major parts. The first three chapters lay the algebraic groundwork for later applications to numerical semigroups. They introduce readers to foundational topics in commutative algebra, homological methods, Cohen–Macaulay and canonical modules—all with a focus on the graded structures that arise naturally in semigroup rings.
Building on the first three chapters, Chapters 4–6 lead to deep results connecting semigroup properties and invariants to algebraic properties and homological data of semigroup rings.
Features
Throughout, the exposition is enriched with illustrative examples, detailed proofs, and exercises to reinforce understanding.
Intended Audience
The book is designed for graduate students in mathematics as well as researchers in algebra, number theory, and combinatorics.
