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.
Rezensionen / Stimmen
"... 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
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Editions-Typ
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Illustrationen
106 s/w Abbildungen
106 Illustrations, black and white
Maße
Höhe: 231 mm
Breite: 160 mm
Dicke: 43 mm
Gewicht
ISBN-13
978-1-4822-3469-5 (9781482234695)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Dr. Rafael H. Villarreal is a professor in the Department of Mathematics at the Centro de Investigacion y de Estudios Avanzados del I.P.N. (Cinvestav-IPN). His research focuses on commutative algebra, algebraic geometry, combinatorics, and computational algebra.
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.
