Overview
- Includes tutorials and exercises for Macaulay 2
- Provides hands-on experience with over 600 exercises
- Broadens understanding of monomial ideals in polynomial rings
Part of the book series: Universitext (UTX)
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Table of contents(9 chapters)
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Monomial Ideals
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Monomial Ideals and Other Areas
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Decomposing Monomial Ideals
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Commutative Algebra and Macaulay2
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
About this book
Reviews
“The present book is thought as a gentle introduction to monomial ideals … . All the chapters contain exercises and Macaulay 2 material for the computational exploration of the presented notions.” (Christos Tatakis, zbMATH 1476.13002, 2022)
“Primarily directed at advanced undergraduates, the text is also a valuable resource for graduate students and researchers who wish to learn more about the subject, providing an introduction to active research topics in combinatorial commutative algebra and its applications. … the authors' presentation of monomial decompositions and their applications is an exciting, enlightening read and will serve an individual reader or class instructor well.” (Timothy B. P. Clark, Mathematical Reviews, October, 2019)
“Each definition includes examples of reasonably common structures … . This style makes the text accessible to advanced undergraduates. … it will be useful to those who work in symbolic computation and theory.” (Paul Cull, Computing Reviews, May 13, 2019)
Authors and Affiliations
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Department of Mathematics, Wake Forest University, Winston-Salem, USA
W. Frank Moore
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Department of Mathematics, Missouri State University, Springfield, USA
Mark Rogers
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School of Mathematical and Statistical Sciences, Clemson University, Clemson, USA
Sean Sather-Wagstaff
About the authors
Mark Rogers is a Professor in the Department of Mathematics at Missouri State University. He earned his PhD from Purdue University, and his area of research is commutative algebra.
Sean Sather-Wagstaff is an Associate Professor in Clemson University’s department of Mathematical Sciences. He earned his PhD from the University of Utah, specializing in homological commutative algebra.
Bibliographic Information
Book Title: Monomial Ideals and Their Decompositions
Authors: W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-96876-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-96874-2Published: 06 November 2018
eBook ISBN: 978-3-319-96876-6Published: 24 October 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XXIV, 387
Number of Illustrations: 55 b/w illustrations
Topics: Commutative Rings and Algebras, Symbolic and Algebraic Manipulation, Associative Rings and Algebras, Category Theory, Homological Algebra, Algebraic Topology, Algebraic Geometry