Monomial Ideals and Their Decompositions

W. Frank Moore is an Associate Professor of Mathematics at Wake Forest University. He earned his PhD from the University of Nebraska-Lincoln, and his research is in the homological algebra of commutative and noncommutative rings.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.

“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)

• -Introduction.- 1. Fundamental Properties of Monomial Ideals . -2. Operations on Monomial Ideals.- 3.  M-Irreducible Ideals and Decompositions.- 4.  Connections with Combinatorics.- 5.  Connections with Other Areas. -6.  Parametric Decompositions of Monomial Ideals.- 7.  Computing M-Irreducible Decompositions.- Appendix A. Foundational Concepts.- Appendix B. Introduction to Macaulay2.- Bibliography.- Index.