Monomial Ideals and Their Decompositions

Häftad, Engelska, 2018

AvW. Frank Moore,Mark Rogers,Sean Sather-Wagstaff

629 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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.

Produktinformation

Utgivningsdatum2018-11-06
Mått155 x 235 x 25 mm
Vikt644 g
FormatHäftad
SpråkEngelska
SerieUniversitext
Antal sidor387
FörlagSpringer International Publishing AG
ISBN9783319968742

Tillhör följande kategorier

Systemvetenskap och AI inom Data och it
Algebra inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

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.

-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.

“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)