Skip to main content
SpringerLink
Log in
Book cover

Algebra II

Noncommutative Rings Identities

  • Book
  • © 1991

Overview

Editors:
  1. A. I. Kostrikin

    1. Steklov Mathematical Institute, Moscow, USSR

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. I. R. Shafarevich

    1. Steklov Mathematical Institute, Moscow, USSR

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 18)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (2 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Noncommutative Rings

    • L. A. Bokhut’, I. V. L’vov, V. K. Kharchenko
    Pages 1-106

  3. Identities

    • Yu. A. Bakhturin, A. Yu. Ol’shanskij
    Pages 107-221

  4. Back Matter

    Pages 223-236
    Download chapter PDF
Back to top

Keywords

About this book

The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge­ 1 bra • Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat­ ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap­ plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al­ gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep­ resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with· polynomial coefficients) often appears in the representation theory of Lie algebras. In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le.

Editors and Affiliations

  • Steklov Mathematical Institute, Moscow, USSR

    A. I. Kostrikin, I. R. Shafarevich

Bibliographic Information

  • Book Title: Algebra II

  • Book Subtitle: Noncommutative Rings Identities

  • Editors: A. I. Kostrikin, I. R. Shafarevich

  • Series Title: Encyclopaedia of Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-642-72899-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-642-72901-0Published: 23 November 2011

  • eBook ISBN: 978-3-642-72899-0Published: 06 December 2012

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: VII, 234

  • Additional Information: Original Russian edition published by VINITI, Moscow 1988

  • Topics: Group Theory and Generalizations

Publish with us

Policies and ethics

Back to top

Search

Navigation