Monomial Algebras
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ISBN-13:
9781482234695
Veröffentl:
2015
Erscheinungsdatum:
26.03.2015
Seiten:
704
Autor:
Rafael Villarreal
Gewicht:
1134 g
Format:
231x160x43 mm
Sprache:
Englisch
Beschreibung:
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.
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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