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Binomial Ideals - Herzog, Jürgen

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        Présentation Binomial Ideals de Herzog, Jürgen Format Broché

         - Livre Littérature Générale

        Livre Littérature Générale - Herzog, Jürgen - 01/01/2019 - Broché - Langue : Anglais

        . .

      • Auteur(s) : Herzog, Jürgen - Ohsugi, Hidefumi - Hibi, Takayuki
      • Editeur : Springer International Publishing Ag
      • Langue : Anglais
      • Parution : 01/01/2019
      • Format : Moyen, de 350g à 1kg
      • Nombre de pages : 344
      • Expédition : 522
      • Dimensions : 23.5 x 15.5 x 1.9
      • ISBN : 9783030070199



      • Résumé :

        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 Gr?bner 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.
        ...

        Biographie:
        J?rgen Herzon is a professor at the University of Duisburg-Essen and coauthor of Monomial Ideals (2011) with Takayuki Hibi.

        Takayuki Hibi is a professor at Osaka University.
        Hidefumi Ohsugi is a professor at Rikkyo University.
        ...

        Sommaire:

        J?rgen Herzog was a professor of mathematics at the University of Duisburg-Essen, Germany. He received his doctorate at Louisiana State University in 1969 and completed his habilitation at the University of Regensburg in 1974. Since 1975, he was a professor at the University of Essen, later Duisburg-Essen, where he retired in 2009. His main research area was in the field of commutative algebra. During the course of his scientific career, he published more than 250 articles and made a significant impact in the development of commutative algebra. J?rgen Herzog sadly passed away on 23 April 2024 before this book could be published. He will be greatly missed in the mathematical community.

        Somayeh Moradi is associate professor of mathematics at Ilam University, Iran. She received her doctorate from Amirkabir University of Technology - Tehran Polytechnic in 2009. She was appointed assistant professor at Ilam University in 2010 and later in 2017 as associate professor. From march 2023 to March 2025, she was the recipient of the Alexander von Humboldt Research Fellowship at the University of Duisburg-Essen. She is also the recipient of the Maryam Mirzakhani Award 2025. Her main research interests lie in commutative algebra and combinatorics.

        Masoomeh Rahimbeigi is a researcher at the University of Duisburg-Essen, Germany. She received her doctorate from the University of Kurdistan, Iran in 2019. Her main research area is in commutative algebra....

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