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  Encyclopedia of Keywords > Integral Domains > Division Rings   Michael Charnine

Keywords and Sections
VECTOR SPACE
RINGS
COMMUTATIVE
FIELDS
INTEGRAL DOMAINS
DIVISION RINGS
Review of Short Phrases and Links

    This Review contains major "Division Rings"- related terms, short phrases and links grouped together in the form of Encyclopedia article.

Definitions

  1. Division rings are very similar to fields - they differ only in that their multiplication is not required to be commutative.

Vector Space

  1. A vector space in GAP is a free left module (see IsFreeLeftModule) over a division ring (see Chapter Fields and Division Rings).

Rings

  1. There is a long FAQ on sets with products (rings), a particular emphasis of which is the study of division rings over the reals. (Web site)

Commutative

  1. Wedderburn's (little) theorem: All finite division rings are commutative and therefore finite fields.

Fields

  1. Of course the general functionality for fields (see Chapter Fields and Division Rings) also applies to finite fields. (Web site)
  2. Division rings used to be called fields in an older usage. (Web site)

Integral Domains

  1. In particular, this applies to all fields, to all integral domains, and to all division rings. (Web site)

Division Rings

  1. Much of linear algebra may be formulated, and remains correct, for (left) modules over division rings instead of vector space s over fields. (Web site)
  2. Much of linear algebra may be formulated, and remains correct, for (left) modules over division rings instead of vector spaces over fields. (Web site)

Categories

  1. Integral Domains
  2. Fields
  3. Commutative
  4. Science > Mathematics > Algebra > Linear Algebra
  5. Encyclopedia of Keywords > Information > Structure > Rings
  6. Books about "Division Rings" in Amazon.com

Book: Keywen Category Structure


  Short phrases about "Division Rings"
  Originally created: April 04, 2011.
  Links checked: January 10, 2013.
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