Binomial ideals

By:

Herzog, Jürgen

Contributor(s):

Series: Graduate texts in mathematicsPublication details: Springer, 2018 Cham, Switzerland :Description: xix; 321p. hb; 25 cmISBN:

9783319953472

Subject(s):

DDC classification:

512.44 HER

Summary: "This textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with a set of exercises and a list of related topics and results that will complement and offer a better understanding of the material presented. Binomial Ideals is suitable for graduate students in courses on commutative algebra, algebraic combinatorics, and statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource."--Page 4 of cover.

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Holdings
Item type	Current library	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	512.44 HER (Browse shelf(Opens below))	1	Available		027909

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Previous	512.4 WIN Cohen-Macaulay rings	512.42 LAU Cohomology of drinfeld modular varieties: part 1. geometry, counting of points and local harmonic analysis	512.42 MIR Determinantal ideals	512.44 HER Binomial ideals	512.44 KUN Introduction to commutative algebra and algebraic geometry	512.44 MIL Combinatorial commutative algebra	512.44 BRE Conference on commutative algebra	Next

Includes bibliographical references (pages 307-315) and index.

"This textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with a set of exercises and a list of related topics and results that will complement and offer a better understanding of the material presented. Binomial Ideals is suitable for graduate students in courses on commutative algebra, algebraic combinatorics, and statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource."--Page 4 of cover.

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