Monomial Algebras

2nd Edition

Rafael Villarreal

Chapman and Hall/CRC
Published March 12, 2018
Reference - 704 Pages - 106 B/W Illustrations
ISBN 9781138894181 - CAT# K32871
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Summary

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.

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