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Monomial Algebras de Rafael Villarreal

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

Autor Rafael Villarreal
en Limba Engleză Paperback – 12 mar 2018
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.
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Specificații

ISBN-13: 9781138894181
ISBN-10: 1138894184
Pagini: 704
Ilustrații: 106 Illustrations, black and white
Dimensiuni: 156 x 234 x 43 mm
Greutate: 0.45 kg
Ediția:2 New edition
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Cuprins

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.

Notă biografică

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.

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

Descriere

This book presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. Along with revising all existing chapters, this edition includes four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs. It also contains two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs.