Binomial Ideals by Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi.
Herzog, Jurgen. 28098
Hibi, Takayuki. 28106
Ohsugi, Hidefumi. 28107
Combinatorics. 28099
Commutative algebra. 28100
Commutative rings. 28101
Convex geometry. 28102
Discrete geometry. 28103
512.44 H44B 23
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.
Switzerland: Springer Nature,
2018.
2018.
2018
Text
XIX, 321 p.
eng
Graduate Texts in Mathematics, 0072-5285 ; 279
Graduate Texts in Mathematics, 279 28108
Binomial ideals
Binomial ideals