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:
    non sort: The
    title: Congruences of a Finite Lattice
    sub title: A Proof-by-Picture Approach
  name:
    name part: Grätzer, George.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXVI, 282 p. online resource.
  abstract: The congruences of a lattice form the congruence lattice. In the past half-century, the study of congruence lattices has become a large and important field with a great number of interesting and deep results and many open problems. This self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presents the major results on congruence lattices of finite lattices featuring the author's signature "Proof-by-Picture" method and its conversion to transparencies. Key features: * Includes the latest findings from a pioneering researcher in the field * Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions * Contains complete proofs, an extensive bibliography and index, and nearly 80 open problems * Additional information provided by the author online at: http://www.maths.umanitoba.ca/homepages/gratzer.html/ The book is appropriate for a one-semester graduate course in lattice theory, yet is also designed as a practical reference for researchers studying lattices.
  table of contents: A Brief Introduction to Lattices -- Basic Concepts -- Special Concepts -- Congruences -- Basic Techniques -- Chopped Lattices -- Boolean Triples -- Cubic Extensions -- Representation Theorems -- The Dilworth Theorem -- Minimal Representations -- Semimodular Lattices -- Modular Lattices -- Uniform Lattices -- Extensions -- Sectionally Complemented Lattices -- Semimodular Lattices -- Isoform Lattices -- Independence Theorems -- Magic Wands -- Two Lattices -- Sublattices -- Ideals -- Tensor Extensions.
  note: by George Grätzer.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Ordered algebraic structures
  subject:
    topic: Mathematical logic
  subject:
    topic: Number theory
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Order, Lattices, Ordered Algebraic Structures
  subject:
    topic: Mathematical Logic and Foundations
  subject:
    topic: Algebra
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Number Theory
  classification: QA172-172.4
  classification: QA171.5
  classification: 511.33
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780817644628
  identifier: http://dx.doi.org/10.1007/0-8176-4462-8
  record info:
    record creation date: 100301
    record change date: 20151204182454.0
    record identifier: 978-0-8176-4462-8