Graduate Texts in Mathematics

Monomial Ideals

Authors: Herzog, Jürgen, Hibi, Takayuki

  • -Theory is complemented by examples and exercises, bringing the reader to a deeper understanding of explored concepts
  • - A useful introduction to the fields of combinatorial and computational commutative algebra, with a special focus on monomial ideals
  • - Only a basic knowledge of commutative algebra is required
see more benefits

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-85729-106-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-85729-105-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-1-4471-2594-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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)

Table of contents (12 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-85729-106-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-85729-105-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-1-4471-2594-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Monomial Ideals
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
260
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Ltd.
eBook ISBN
978-0-85729-106-6
DOI
10.1007/978-0-85729-106-6
Hardcover ISBN
978-0-85729-105-9
Softcover ISBN
978-1-4471-2594-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVI, 305
Topics