Rafael Villarreal

Monomial Algebras

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis Ltd (Sales)
• 2nd edition
• Seitenzahl: 704
• Erscheinungstermin: 26. März 2015
• Englisch
• Abmessung: 231mm x 160mm x 43mm
• Gewicht: 1134g
• ISBN-13: 9781482234695
• ISBN-10: 1482234696
• Artikelnr.: 41758290

Autorenporträt

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.

Inhaltsangabe

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.

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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.

Rezensionen

"... 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