
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
 Division rings are very similar to fields  they differ only in that their multiplication is not required to be commutative.
 A vector space in GAP is a free left module (see IsFreeLeftModule) over a division ring (see Chapter Fields and Division Rings).
 There is a long FAQ on sets with products (rings), a particular emphasis of which is the study of division rings over the reals.
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 Wedderburn's (little) theorem: All finite division rings are commutative and therefore finite fields.
 Of course the general functionality for fields (see Chapter Fields and Division Rings) also applies to finite fields.
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 Division rings used to be called fields in an older usage.
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 In particular, this applies to all fields, to all integral domains, and to all division rings.
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Division Rings
 Much of linear algebra may be formulated, and remains correct, for (left) modules over division rings instead of vector space s over fields.
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 Much of linear algebra may be formulated, and remains correct, for (left) modules over division rings instead of vector spaces over fields.
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Categories
 Integral Domains
 Fields
 Commutative
 Science > Mathematics > Algebra > Linear Algebra
 Encyclopedia of Keywords > Information > Structure > Rings

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