Numerical Semigroups
A Commutative Algebra Approach
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Beschreibung
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. 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.
Throughout, the exposition is enriched with illustrative examples, detailed proofs, and exercises to reinforce understanding. The book is designed for graduate students in mathematics as well as researchers in algebra, number theory, and combinatorics.
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. 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.
Throughout, the exposition is enriched with illustrative examples, detailed proofs, and exercises to reinforce understanding. The book is designed for graduate students in mathematics as well as researchers in algebra, number theory, and combinatorics.
Bridges numerical semigroups and commutative algebra in a systematic way Presents concepts in a way that is accessible to non-specialists in commutative algebra Offers the main trends and directions of research
Autor*in
Jürgen Herzog
Themen in »Numerical Semigroups«
Cohen-Macaulay Module Graded Rings and Modules Free Resolution Canonical Module Koszul Complex Local Cohomology Gorenstein ring Affine and Numerical Semigroup Ring Frobenius Number Pseudo Frobenius Number Canonical Trace Symmetric Numerical Semigroup