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  SPECIFICATION
MONOMIAL ALGEBRAS 2e(pb) 2018
Author: VILLARREAL
ISBN: 9781138894181
Year: 2018
Publisher: CRC PRESS
Category: MATHEMATICS
Edition: 2
Format: Paperback
Language: English
Pages: 704
 ABOUT THE TITLE
Features
•Presents computational and combinatorial methods in commutative algebra
•Shows how to solve a variety of problems of monomial algebras
•Covers various affine and graded rings, including Cohen–Macaulay, complete intersection, and normal
•Examines their basic algebraic invariants, such as multiplicity, Betti numbers, projective dimension, and Hilbert polynomial
•Contains over 550 exercises and over 50 examples, many of which illustrate the use of computer algebra systems
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.

Author(s) Bio
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.



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