Monomial Ideals

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...

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Détails bibliographiques
Cote:Libro Electrónico
Auteurs principaux: Herzog, Jürgen (Auteur), Hibi, Takayuki (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: London : Springer London : Imprint: Springer, 2011.
Édition:1st ed. 2011.
Collection:Graduate Texts in Mathematics, 260
Sujets:
Commutative algebra.
Commutative rings.
Commutative Rings and Algebras.
Accès en ligne:Texto Completo
Table des matières:
  • 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.

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