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The Resource Monomial Ideals and Their Decompositions, by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff, (electronic resource)

Monomial Ideals and Their Decompositions, by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff, (electronic resource)

Creator
Author
Contributor
Summary
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. .--
Language
eng
Work
Publication
Extent
1 online resource (XXIV, 387 pages)
Contents
  • -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.
Isbn
9783319968766
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-96876-6
Instance
Label
Monomial Ideals and Their Decompositions
Title
Monomial Ideals and Their Decompositions
Statement of responsibility
by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff
Creator
Contributor
Author
Subject
Language
eng
Summary
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. .--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Moore, W Frank
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Rogers, Mark.
  • Sather-Wagstaff, Sean.
Series statement
  • Springer eBooks
  • Springer eBooks.
  • Universitext,
http://library.link/vocab/subjectName
  • Algebra
  • Algebra
  • Algebraic topology
  • Geometry, algebraic
Label
Monomial Ideals and Their Decompositions, by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-96876-6
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
-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.
Control code
978-3-319-96876-6
Dimensions
unknown
Extent
1 online resource (XXIV, 387 pages)
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319968766
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
55 illustrations
Specific material designation
remote
System control number
(OCoLC)1060523540
Label
Monomial Ideals and Their Decompositions, by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-96876-6
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
-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.
Control code
978-3-319-96876-6
Dimensions
unknown
Extent
1 online resource (XXIV, 387 pages)
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319968766
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
55 illustrations
Specific material designation
remote
System control number
(OCoLC)1060523540

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