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- 704 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Monomial Algebras
Book details
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About This Book
Monomial Algebras, Second Edition 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 Second Edition
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- Four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs
- Two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs
- Full revisions of existing chapters to provide an up-to-date account of the subject
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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Yes, you can access Monomial Algebras by Rafael Villarreal in PDF and/or ePUB format, as well as other popular books in Matemáticas & Matemáticas general. We have over one million books available in our catalogue for you to explore.
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Table of contents
- Front Cover
- Contents
- Preface
- Preface to First Edition
- 1. Polyhedral Geometry and Linear Optimization
- 2. Commutative Algebra
- 3. Affine and Graded Algebras
- 4. Rees Algebras and Normality
- 5. Hilbert Series
- 6. Stanley–Reisner Rings and Edge Ideals of Clutters
- 7. Edge Ideals of Graphs
- 8. Toric Ideals and Affine Varieties
- 9. Monomial Subrings
- 10. Monomial Subrings of Graphs
- 11. Edge Subrings and Combinatorial Optimization
- 12. Normality of Rees Algebras of Monomial Ideals
- 13. Combinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters
- 14. Combinatorial Optimization and Blowup Algebras
- Appendix Graph Diagrams
- Bibliography