Overview
- Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text
- Provides a quick and useful introduction to research spanning the fields of combinatorial and computational commutative algebra, with a special focus on monomial ideals
- Only a basic knowledge of commutative algebra is required, making this accessible to specialists and non-specialists alike
Part of the book series: Graduate Texts in Mathematics (GTM, volume 260)
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Table of contents (12 chapters)
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Front Matter
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Gröbner bases
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Front Matter
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Hilbert functions and resolutions
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Front Matter
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Combinatorics
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Front Matter
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Back Matter
Keywords
About this book
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 I offers a quick introduction to the modern theory of Gröbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal—Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text.
Self-contained and concise, this book will appeal to a wide range of readers, including PhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowledge of commutative algebra.
Since their first meeting in 1985, Juergen Herzog (Universität Duisburg-Essen, Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in this monograph.
Reviews
From the reviews:
“The authors … who themselves have played an important, often crucial, role in recent developments of the subject, make an ideal co-author pairing for composing a book with such a comprehensive choice of material, including the latest achievements. It should serve as a useful resource for researchers in both commutative algebra and combinatorics. … The presentation of the material is distinctive for its clarity and elegant style. … The text can serve nicely as a basis for a couple of graduate courses in two semesters.” (Rahim Zaare-Nahandi, Mathematical Reviews, Issue 2011 k)Authors and Affiliations
Bibliographic Information
Book Title: Monomial Ideals
Authors: Jürgen Herzog, Takayuki Hibi
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-0-85729-106-6
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Ltd. 2011
Hardcover ISBN: 978-0-85729-105-9Published: 07 October 2010
Softcover ISBN: 978-1-4471-2594-5Published: 01 December 2012
eBook ISBN: 978-0-85729-106-6Published: 28 September 2010
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVI, 305
Topics: Commutative Rings and Algebras