Monomial Ideals And Their Decompositions

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Monomial Ideals and Their Decompositions

W. Frank Moore,Mark Rogers,Sean Sather-Wagstaff
Monomial Ideals and Their Decompositions Book PDF

Author : W. Frank Moore,Mark Rogers,Sean Sather-Wagstaff
Publisher : Springer
Page : 387 pages
File Size : 43,7 Mb
Release : 2018-10-24
Category : Mathematics
ISBN : 9783319968766

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Monomial Ideals and Their Decompositions by W. Frank Moore,Mark Rogers,Sean Sather-Wagstaff Pdf

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.

Monomial Ideals and Their Decompositions

W. Frank Moore,Mark Rogers,Sean Sather-Wagstaff
Monomial Ideals and Their Decompositions Book PDF

Author : W. Frank Moore,Mark Rogers,Sean Sather-Wagstaff
Publisher : Unknown
Page : 387 pages
File Size : 42,8 Mb
Release : 2018
Category : Commutative algebra
ISBN : 3319968750

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Monomial Ideals and Their Decompositions by W. Frank Moore,Mark Rogers,Sean Sather-Wagstaff Pdf

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. . .

Monomial Ideals, Computations and Applications

Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Monomial Ideals Computations and Applications Book PDF

Author : Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Publisher : Springer
Page : 194 pages
File Size : 43,8 Mb
Release : 2013-08-24
Category : Mathematics
ISBN : 9783642387425

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Monomial Ideals, Computations and Applications by Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón Pdf

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps
Singularities Algebraic Geometry Commutative Algebra and Related Topics Book PDF

Author : Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps
Publisher : Springer
Page : 604 pages
File Size : 55,8 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9783319968278

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics by Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps Pdf

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.

Monomial Ideals

Jürgen Herzog,Takayuki Hibi
Monomial Ideals Book PDF

Author : Jürgen Herzog,Takayuki Hibi
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 40,7 Mb
Release : 2010-09-28
Category : Mathematics
ISBN : 9780857291066

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Monomial Ideals by Jürgen Herzog,Takayuki Hibi Pdf

This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Gröbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal—Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text. Self-contained and concise, this book will appeal to a wide range of readers, including PhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowledge of commutative algebra. Since their first meeting in 1985, Juergen Herzog (Universität Duisburg-Essen, Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in this monograph.

Binomial Ideals

Jürgen Herzog,Takayuki Hibi,Hidefumi Ohsugi
Binomial Ideals Book PDF

Author : Jürgen Herzog,Takayuki Hibi,Hidefumi Ohsugi
Publisher : Springer
Page : 321 pages
File Size : 54,9 Mb
Release : 2018-09-28
Category : Mathematics
ISBN : 9783319953496

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Binomial Ideals by Jürgen Herzog,Takayuki Hibi,Hidefumi Ohsugi Pdf

This textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results, and applications of binomial ideals to other areas of mathematics. The book begins with a brief, self-contained overview of the modern theory of Gröbner bases and the necessary algebraic and homological concepts from commutative algebra. Binomials and binomial ideals are then considered in detail, along with a short introduction to convex polytopes. Chapters in the remainder of the text can be read independently and explore specific aspects of the theory of binomial ideals, including edge rings and edge polytopes, join-meet ideals of finite lattices, binomial edge ideals, ideals generated by 2-minors, and binomial ideals arising from statistics. Each chapter concludes with a set of exercises and a list of related topics and results that will complement and offer a better understanding of the material presented. Binomial Ideals is suitable for graduate students in courses on commutative algebra, algebraic combinatorics, and statistics. Additionally, researchers interested in any of these areas but familiar with only the basic facts of commutative algebra will find it to be a valuable resource.

Integral Closure of Ideals, Rings, and Modules

Craig Huneke,Irena Swanson
Integral Closure of Ideals Rings and Modules Book PDF

Author : Craig Huneke,Irena Swanson
Publisher : Cambridge University Press
Page : 446 pages
File Size : 50,5 Mb
Release : 2006-10-12
Category : Mathematics
ISBN : 9780521688604

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Integral Closure of Ideals, Rings, and Modules by Craig Huneke,Irena Swanson Pdf

Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Combinatorial Commutative Algebra

Ezra Miller,Bernd Sturmfels
Combinatorial Commutative Algebra Book PDF

Author : Ezra Miller,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 54,5 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 0387237070

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Combinatorial Commutative Algebra by Ezra Miller,Bernd Sturmfels Pdf

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Algebraic and Combinatorial Computational Biology

Raina Robeva,Matthew Macauley
Algebraic and Combinatorial Computational Biology Book PDF

Author : Raina Robeva,Matthew Macauley
Publisher : Academic Press
Page : 434 pages
File Size : 46,8 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9780128140697

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Algebraic and Combinatorial Computational Biology by Raina Robeva,Matthew Macauley Pdf

Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences. Integrates a comprehensive selection of tools from computational biology into educational or research programs Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations Contains scalable material for use in undergraduate and graduate-level classes and research projects Introduces the reader to freely-available professional software Supported by illustrative datasets and adaptable computer code

Surveys in Differential-Algebraic Equations II

Achim Ilchmann,Timo Reis
Surveys in Differential Algebraic Equations II Book PDF

Author : Achim Ilchmann,Timo Reis
Publisher : Springer
Page : 339 pages
File Size : 48,5 Mb
Release : 2014-12-04
Category : Mathematics
ISBN : 9783319110509

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Surveys in Differential-Algebraic Equations II by Achim Ilchmann,Timo Reis Pdf

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Observers for DAEs - DAEs in chemical processes - Optimal control of DAEs - DAEs from a functional-analytic viewpoint - Algebraic methods for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Monomial Algebras

Rafael Villarreal
Monomial Algebras Book PDF

Author : Rafael Villarreal
Publisher : CRC Press
Page : 704 pages
File Size : 53,5 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9781482234701

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Monomial Algebras by Rafael Villarreal Pdf

Monomial Algebras, Second Edition presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. It emphasizes square-free monomials and the corresponding graphs, clutters, or hypergraphs. New to the Second Edition Four new chapters that focus on the algebraic properties of blowup algebras in combinatorial optimization problems of clutters and hypergraphs Two new chapters that explore the algebraic and combinatorial properties of the edge ideal of clutters and hypergraphs Full revisions of existing chapters to provide an up-to-date account of the subject Bringing together several areas of pure and applied mathematics, this book shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs. It directly links the algebraic properties of monomial algebras to combinatorial structures (such as simplicial complexes, posets, digraphs, graphs, and clutters) and linear optimization problems.

Computations and Combinatorics in Commutative Algebra

Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Computations and Combinatorics in Commutative Algebra Book PDF

Author : Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Publisher : Springer
Page : 127 pages
File Size : 51,6 Mb
Release : 2017-03-14
Category : Mathematics
ISBN : 9783319513195

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Computations and Combinatorics in Commutative Algebra by Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón Pdf

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and Combinatorics in Commutative Algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.

Gröbner Bases and Convex Polytopes

Bernd Sturmfels
Gr bner Bases and Convex Polytopes Book PDF

Author : Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 44,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804872

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Gröbner Bases and Convex Polytopes by Bernd Sturmfels Pdf

This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry.

Computational Commutative Algebra 2

Martin Kreuzer,Lorenzo Robbiano
Computational Commutative Algebra 2 Book PDF

Author : Martin Kreuzer,Lorenzo Robbiano
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 50,7 Mb
Release : 2005-11-04
Category : Mathematics
ISBN : 9783540282969

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Computational Commutative Algebra 2 by Martin Kreuzer,Lorenzo Robbiano Pdf

"The second volume of the authors’ ‘Computational commutative algebra’...covers on its 586 pages a wealth of interesting material with several unexpected applications. ... an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications." --ZENTRALBLATT MATH

Commutative Algebra

David Eisenbud
Commutative Algebra Book PDF

Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 55,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253501

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Commutative Algebra by David Eisenbud Pdf

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.