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: Difference Algebra
  name:
    name part: Levin, Alexander.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ne
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 521 p. online resource.
  abstract: Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields in much the same way as the classical algebraic geometry arose from the study of polynomial equations with numerical coefficients. The first stage of the development of the theory is associated with its founder J. F. Ritt (1893 - 1951) and R. Cohn whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years. Nowadays, difference algebra has overgrew the frame of the theory of ordinary algebraic difference equations and appears as a rich theory with applications to the study of equations in finite differences, functional equations, differential equations with delay, algebraic structures with operators, group and semigroup rings. This book reflects the contemporary level of difference algebra; it contains a systematic study of partial difference algebraic structures and their applications, as well as the coverage of the classical theory of ordinary difference rings and field extensions. The monograph is intended for graduate students and researchers in difference and differential algebra, commutative algebra, ring theory, and algebraic geometry. It will be also of interest to researchers in computer algebra, theory of difference equations and equations of mathematical physics. The book is self-contained; it requires no prerequisites other than knowledge of basic algebraic concepts and mathematical maturity of an advanced undergraduate.
  table of contents: Preliminaries -- Basic Concepts of Difference Algebra -- Difference Modules -- Difference Field Extensions -- Compatibility, Replicability, and Monadicity -- Difference Kernels over Partial Difference Fields. Difference Valuation Rings -- Systems of Algebraic Difference Equations -- Elements of the Difference Galois Theory.
  note: by Alexander Levin.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Commutative algebra
  subject:
    topic: Commutative rings
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Difference equations
  subject:
    topic: Functional equations
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Field Theory and Polynomials
  subject:
    topic: Commutative Rings and Algebras
  subject:
    topic: Difference and Functional Equations
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Algebra and Applications ; 8
  identifier: 9781402069475
  identifier: http://dx.doi.org/10.1007/978-1-4020-6947-5
  record info:
    record creation date: 100301
    record change date: 20151204180518.0
    record identifier: 978-1-4020-6947-5