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: Polytopes, Rings, and K-Theory
  name:
    name part: Gubeladze, Joseph.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Bruns, Winfried.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2009
    edition: 1.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 461 p. 52 illus. online resource.
  abstract: This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphism problems and automorphism groups, homological properties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. This monograph has been written with a view towards graduate students and researchers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, also specialists in lattice polytopes and related objects will find an up-to-date discussion of affine monoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructive approach wherever possible. Winfried Bruns is Professor of Mathematics at Universität Osnabrück. Joseph Gubeladze is Professor of Mathematics at San Francisco State University.
  table of contents: I Cones, monoids, and triangulations -- Polytopes, cones, and complexes -- Affine monoids and their Hilbert bases -- Multiples of lattice polytopes -- II Affine monoid algebras -- Monoid algebras -- Isomorphisms and automorphisms -- Homological properties and Hilbert functions -- Gr#x00F6;bner bases, triangulations, and Koszul algebras -- III K-theory -- Projective modules over monoid rings -- Bass#x2013;Whitehead groups of monoid rings -- Varieties.
  note: by Joseph Gubeladze, Winfried Bruns.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Commutative algebra
  subject:
    topic: Commutative rings
  subject:
    topic: K-theory
  subject:
    topic: Convex geometry
  subject:
    topic: Discrete geometry
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Commutative Rings and Algebras
  subject:
    topic: K-Theory
  subject:
    topic: Convex and Discrete Geometry
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9780387763569
  identifier: http://dx.doi.org/10.1007/b105283
  record info:
    record creation date: 100301
    record change date: 20151204183718.0
    record identifier: 978-0-387-76356-9