Description
Monomial Ideals and Their Decompositions, 1st ed. 2018
Universitext Series
Authors: Moore W. Frank, Rogers Mark, Sather-Wagstaff Sean
Language: EnglishSubject for Monomial Ideals and Their Decompositions:
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
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Description
/li>Contents
/li>Biography
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-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.
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.
Includes tutorials and exercises for Macaulay 2
Provides hands-on experience with over 600 exercises
Broadens understanding of monomial ideals in polynomial rings