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: Quadratic and Hermitian Forms over Rings
  name:
    name part: Knus, Max-Albert.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 1991
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xi, 524 pages)
  abstract: This book presents the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial properties of the theory. It is not an encyclopedic survey. It stresses the algebraic aspects of the theory and avoids - within reason - overlapping with other books on quadratic forms (like those of Lam, Milnor-Husemöller and Scharlau). One important tool is descent theory with the corresponding cohomological machinery. It is used to define the classical invariants of quadratic forms, but also for the study of Azmaya algebras, which are fundamental in the theory of Clifford algebras. Clifford algebras are applied, in particular, to treat in detail quadratic forms of low rank and their spinor groups. Another important tool is algebraic K-theory, which plays the role that linear algebra plays in the case of forms over fields. The book contains complete proofs of the stability, cancellation and splitting theorems in the linear and in the unitary case. These results are applied to polynomial rings to give quadratic analogues of the theorem of Quillen and Suslin on projective modules. Another, more geometric, application is to Witt groups of regular rings and Witt groups of real curves and surfaces.
  note: by Max-Albert Knus.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Number theory
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Mathematics
  subject:
    topic: Number theory
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics ; 294
  identifier: 9783642754012 (electronic bk.)
  identifier: 3642754015 (electronic bk.)
  identifier: 9783642754036
  identifier: 3642754031
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260422171017.2
    record identifier: in00003568707
    language of cataloging:
      language term: eng