Monomial Ideals by Takayuki Hibi (English) Hardcover Book

Description: Monomial Ideals by Takayuki Hibi, JÜrgen Herzog 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. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. Notes Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the textProvides a quick and useful introduction to research spanning the fields of combinatorial and computational commutative algebra, with a special focus on monomial idealsOnly a basic knowledge of commutative algebra is required, making this accessible to specialists and non-specialists alike Back Cover 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 Gr 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 Review 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) Review Quote 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) Feature -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 Details ISBN085729105X Pages 305 Series Graduate Texts in Mathematics Language English ISBN-10 085729105X ISBN-13 9780857291059 Media Book Format Hardcover Series Number 260 Publisher Springer London Ltd Year 2010 Author JÜrgen Herzog Short Title MONOMIAL IDEALS Imprint Springer London Ltd Place of Publication England Country of Publication United Kingdom DEWEY 512.42 DOI 10.1007/978-0-85729-106-6 AU Release Date 2010-10-07 NZ Release Date 2010-10-07 UK Release Date 2010-10-07 Edition Description 2011 ed. Edition 2011th Publication Date 2010-10-07 Alternative 9781447125945 Illustrations XVI, 305 p. Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96247203;

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