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101 0 $aeng
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181   $ctxt$2rdacontent
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200 10$aBinomial Ideals /$fby Jürgen Herzog, Takayuki Hibi, Hidefumi Ohsugi
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XIX, 321 p. 55 illus., 4 illus. in color.) 
225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v279
311   $a3-319-95347-8 
327   $aPart I: Basic Concepts -- Polynomial Rings and Gröbner Bases -- Review of Commutative Algebra -- Part II:Binomial Ideals and Convex Polytopes -- Introduction to Binomial Ideals -- Convex Polytopes and Unimodular Triangulations -- Part III. Applications in Combinatorics and Statistics- Edge Polytopes and Edge Rings -- Join-Meet Ideals of Finite Lattices -- Binomial Edge Ideals and Related Ideals -- Ideals Generated by 2-Minors -- Statistics -- References -- Index.
330   $aThis textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with a set of exercises and a list of related topics and results that will complement and offer a better understanding of the material presented. Binomial Ideals is suitable for graduate students in courses on commutative algebra, algebraic combinatorics, and statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource.
410  0$aGraduate Texts in Mathematics,$x0072-5285 ;$v279
606   $aCommutative algebra
606   $aCommutative rings
606   $aConvex geometry 
606   $aDiscrete geometry
606   $aCombinatorics
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aConvex geometry .
615  0$aDiscrete geometry.
615  0$aCombinatorics.
615 14$aCommutative Rings and Algebras.
615 24$aConvex and Discrete Geometry.
615 24$aCombinatorics.
676   $a512.9
700   $aHerzog$b Jürgen$4aut$4http://id.loc.gov/vocabulary/relators/aut$0732133
702   $aHibi$b Takayuki$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aOhsugi$b Hidefumi$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300140403321
996   $aBinomial Ideals$91991481
997   $aUNINA