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  • Format: ePub

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
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Produktbeschreibung
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.


Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

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.

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