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Mathematics - Algebra | Hilbert Functions of Filtered Modules

Hilbert Functions of Filtered Modules

Rossi, Maria Evelina, Valla, Giuseppe

2010, XVIII, 100p.

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  • Provides a unique perspective on the topic
  • Covers Hilbert functions -- a topic of increasing interest
  • Presents numerous examples that help readers understand the concepts discussed
  • Includes new developments and easier proofs of classical results
Hilbert functions play major parts in Algebraic Geometry and Commutative Algebra, and are also becoming increasingly important in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one book a broad range of new developments in this theory by using a unifying approach which yields self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of this work. The material is intended for graduate students and researchers who are interested in Commutative Algebra, particularly in the theory of the Hilbert functions and related topics.

Content Level » Graduate

Keywords » Associated graded module - Filtration - Hilbert coefficients - Hilbert function - Superficial element - algebra

Related subjects » Algebra

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