An introduction to the methods used to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings, and toric varieties. It emphasizes square-free quadratics and effective computational methods, and applies a combinatorial description of the integral closure of the corresponding monomial subring to graph theory.

Monomial Algebras (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Science & Math

Villarreal, Rafael

Mathematics

CRC-Press

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 <ul>
<li>Four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs</li> <li>Two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs </li> <li>Full revisions of existing chapters to provide an up-to-date account of the subject</li> </ul> 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.

Routledge

Chapman and Hall/CRC

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Books by Villarreal, Rafael

See the best price to sell, buy, or rent books by Villarreal, Rafael. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Monomial Algebras (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Monomial Algebras (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Monomial Algebras (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)