Monomial Algebras

Rafael Villarreal (Autor)

Buch | Hardcover

704 Seiten

2015 | 2nd edition
Chapman & Hall/CRC (Verlag)
978-1-4822-3469-5 (ISBN)

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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.

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.

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.

Reihe/Serie	Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Zusatzinfo	106 Illustrations, black and white
Sprache	englisch
Maße	156 x 234 mm
Gewicht	1138 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-4822-3469-6 / 1482234696
ISBN-13	978-1-4822-3469-5 / 9781482234695
Zustand	Neuware