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Monomial Ideals and Their Decompositions

  • W. Frank Moore
  • Mark Rogers
  • Sean Sather-Wagstaff

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Monomial Ideals

    1. Front Matter
      Pages 1-3
    2. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 5-32
    3. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 33-79
    4. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 81-109
  3. Monomial Ideals and Other Areas

    1. Front Matter
      Pages 111-112
    2. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 115-159
    3. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 161-216
  4. Decomposing Monomial Ideals

    1. Front Matter
      Pages 217-218
    2. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 221-260
    3. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 261-292
  5. Commutative Algebra and Macaulay2

    1. Front Matter
      Pages 293-294
    2. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 297-329
    3. W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
      Pages 331-347
  6. Back Matter
    Pages 349-387

About this book

Introduction

This textbook on combinatorial commutative algebra focuses on properties of monomial ideals in polynomial rings and their connections with other areas of mathematics such as combinatorics, electrical engineering, topology, geometry, and homological algebra. Aimed toward advanced undergraduate students and graduate students who have taken a basic course in abstract algebra that includes polynomial rings and ideals, this book serves as a core text for a course in combinatorial commutative algebra or as preparation for more advanced courses in the area.  The text contains over 600 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a firsthand introduction to the computer algebra system Macaulay2 with tutorials and exercises for most sections of the text, preparing them for significant computational work in the area. Connections to non-monomial areas of abstract algebra, electrical engineering, combinatorics and other areas of mathematics are provided which give the reader a sense of how these ideas reach into other areas.

 

Keywords

Macaulay 2 combinatorial commutative algebra irreducible decompositions monomial ideals polynomial rings simplicial complexes modifying monomial ideals decompositions of monomial ideals vertex covers edge ideal construction of Villarreal m-irreducible decompositions parametric decompositions algorithms commutative algebra Dickson’s Lemma Stanley-Reisner ideals Phasor Measurement Units Cohen-Macaulayness Hilbert functions

Authors and affiliations

  • W. Frank Moore
    • 1
  • Mark Rogers
    • 2
  • Sean Sather-Wagstaff
    • 3
  1. 1.Department of MathematicsWake Forest UniversityWinston-SalemUSA
  2. 2.Department of MathematicsMissouri State UniversitySpringfieldUSA
  3. 3.School of Mathematical and Statistical SciencesClemson UniversityClemsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-96876-6
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-96874-2
  • Online ISBN 978-3-319-96876-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site