Monomial Ideals

• Main Authors: Herzog, Jürgen (Author), Hibi, Takayuki (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2011.
• Subjects: Mathematics.; Commutative algebra.; Commutative rings.; Commutative Rings and Algebras.

This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part...

Table of Contents:

• Part I Gröbner bases: Monomial Ideals
• A short introduction to Gröbner bases
• Monomial orders and weights
• Generic initial ideals
• The exterior algebra
• Part II: Hilbert functions and resolutions
• Hilbert functions and the theorems of Macaulay and Kruskal-Katona
• Resolutions of monomial ideals and the Eliahou-Kervaire formula
• Alexander duality and resolutions
• Part III Combinatorics: Alexander duality and finite graphs
• Powers of monomial ideals
• Shifting theory
• Discrete Polymatroids
• Some homological algebra
• Geometry.