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Monomial Algebras de Rafael H. Villarreal

Monomial Algebras: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Autor Rafael H. Villarreal
en Limba Engleză Hardback – 15 apr 2026
Monomial Algebras presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. It emphasizes square-free monomials and the corresponding graphs, clutters, or hypergraphs.
New to the Third Edition
·       Two full new chapters covering linear and Reed–Muller-type codes (chapter 9), and the containment problem and the resurgence of ideals (chapter 16)
·       Extensive addition of new sections throughout the existing chapters to bring the book up-to-date and make it even more comprehensive
·       A new appendix detailing software procedures for use alongside the book.
Bringing together several areas of pure and applied mathematics, this book shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs. It directly links the algebraic properties of monomial algebras to combinatorial structures (such as simplicial complexes, posets, digraphs, graphs, and clutters) and linear optimization problems.
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Specificații

ISBN-13: 9781041065296
ISBN-10: 1041065299
Pagini: 778
Ilustrații: 138
Dimensiuni: 178 x 254 mm
Greutate: 1.14 kg
Ediția:3. Auflage
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Public țintă

Academic and Postgraduate

Cuprins

Preface 1 Polyhedral Geometry and Linear Optimization 2 Commutative Algebra 3 Affine and Graded Algebras 4 Rees Algebras and Normality 5 Hilbert Series and Gorenstein Rings 6 Stanley–Reisner Rings and Edge Ideals 7 Edge Ideals of Graphs 8 Toric Ideals and Affine Varieties 9 Linear and Reed–Muller Type Codes 10 Monomial Subrings 11 Monomial Subrings of Graphs 12 Edge Subrings and Combinatorial Optimization 13 Normality of Rees Algebras of Monomial Ideals 14 Combinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters 15 Combinatorial Optimization and Blowup Algebras 16 The Containment Problem and the Resurgence of Ideals A Procedures for Macaulay2 and Normaliz B Graph Diagrams Bibliography Notation Index Index

Notă biografică

Rafael H. Villarreal is a Professor at Centro de Investigaci´on y de Estudios Avanzados del Instituto Polit´ecnico Nacional (Cinvestav), earned a Ph.D. degree from Rutgers University(1986). He has published 102 research papers in collaboration with 60 co-authors from various countries, has supervised 11 doctoral dissertations, and has systematically employed combinatorial and computational methods in commutative algebra, and its relation to toric ideals, polyhedral geometry, evaluation codes, combinatorial optimization, algebraic graph theory, graphs and clutters, and topics on monomial Cremona transformations.

Descriere

Monomial Algebras presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras

Recenzii

"… an introduction to algebraic, combinatorial, and computational aspects of monomial ideals. In the second edition, a full revision of all the chapters has been made."
—Zentralblatt MATH 1325