rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Monomial Ideals and Their Decompositions
  name:
    name part: Moore, W. Frank.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Rogers, Mark.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Sather-Wagstaff, Sean.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXIV, 387 p. 55 illus. online resource.
  abstract: 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. . .
  table of 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. .
  note: by W. Frank Moore, Mark Rogers, Sean Sather-Wagstaff.
  subject:
    topic: Commutative algebra
  subject:
    topic: Commutative rings
  subject:
    topic: Computer science-Mathematics
  subject:
    topic: Associative rings
  subject:
    topic: Rings (Algebra)
  subject:
    topic: Category theory (Mathematics)
  subject:
    topic: Homological algebra
  subject:
    topic: Algebraic topology
  subject:
    topic: Algebraic geometry
  subject:
    topic: Commutative Rings and Algebras
  subject:
    topic: Symbolic and Algebraic Manipulation
  subject:
    topic: Associative Rings and Algebras
  subject:
    topic: Category Theory, Homological Algebra
  subject:
    topic: Algebraic Topology
  subject:
    topic: Algebraic Geometry
  classification: QA251.3
  classification: 512.44
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Universitext
  identifier: 9783319968766
  identifier: https://doi.org/10.1007/978-3-319-96876-6
  record info:
    record creation date: 181024
    record change date: 20191220125831.0
    record identifier: 978-3-319-96876-6