Description
Monomial Algebras (2nd Ed.)
Chapman & Hall/CRC Monographs and Research Notes in Mathematics Series
Author: Villarreal Rafael
Language: EnglishSubjects for Monomial Algebras:
Keywords
Polynomial Ring; affine and graded rings; Toric Ideal; algebraic invariants; Rees Algebras; clutters and hypergraphs; Square Free Monomials; combinatorial optimization problems; Minimal Vertex Covers; commutative algebra; Edge Ideal; computational and combinatorial methods; Monomial Ideal; computer algebra systems; Vertex Set; linear optimization; Square Free Monomial Ideal; monomial algebras and their ideals; Vertex Cover; polyhedral geometry; Hilbert Function; square-free monomials; Independent Set; Bipartite Graph; Incidence Matrix; Hilbert Series; Hilbert Basis; Edge Cone; Divisor Class Group; Irreducible Representation; Stanley Reisner Ring; Integral Optimum Solution; Odd Cycles; Cohen Macaulay Ring; Extended Rees Algebra; Perfect Graph
Publication date: 03-2015
· 15.6x23.4 cm · Hardback
Publication date: 03-2018
· 15.6x23.4 cm · Paperback
Description
/li>Contents
/li>Biography
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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
- 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.
Polyhedral Geometry and Linear Optimization. Commutative Algebra. Affine and Graded Algebras. Rees Algebras and Normality. Hilbert Series. Stanley–Reisner Rings and Edge Ideals of Clutters. Edge Ideals of Graphs. Toric Ideals and Affine Varieties. Monomial Subrings. Monomial Subrings of Graphs. Edge Subrings and Combinatorial Optimization. Normality of Rees Algebras of Monomial Ideals. Combinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters. Combinatorial Optimization and Blowup Algebras. Appendix. Bibliography. Notation Index. Index.
Dr. Rafael H. Villarreal is a professor in the Department of Mathematics at the Centro de Investigación y de Estudios Avanzados del I.P.N. (Cinvestav-IPN). His research focuses on commutative algebra, algebraic geometry, combinatorics, and computational algebra.
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