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: Exercises in Modules and Rings
  name:
    name part: Lam, T. Y.
    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: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 414 p. online resource.
  abstract: For the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie’s theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita’s classical theory of category dualities and equivalences. Each of the nineteen sections begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements, generalizations, and latent connections to other problems. This volume is designed as a problem book for the author’s Lectures on Modules and Rings (Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as a source for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of the author’s lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classical Ring Theory (Springer, 2003) offer to the mathematics community the fullest and most comprehensive reference to date for problem solving in the theory of modules and rings.
  table of contents: Free Modules, Projective, and Injective Modules -- Flat Modules and Homological Dimensions -- More Theory of Modules -- Rings of Quotients -- More Rings of Quotients -- Frobenius and Quasi-Frobenius Rings -- Matrix Rings, Categories of Modules and Morita Theory.
  note: by T. Y. Lam.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Associative rings
  subject:
    topic: Rings (Algebra)
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Associative Rings and Algebras
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Problem Books in Mathematics
  identifier: 9780387488998
  identifier: http://dx.doi.org/10.1007/978-0-387-48899-8
  record info:
    record creation date: 100301
    record change date: 20151204175259.0
    record identifier: 978-0-387-48899-8