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fraction field (Definition)

Given an integral domain $ R$, the fraction field of $ R$ is the localization $ S^{-1} R$ of $ R$ with respect to the multiplicative set $ S = R \setminus \{0\}$. It is always a field.



"fraction field" is owned by djao.
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See Also: localization, rational function

Other names:  field of fractions, quotient field
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Cross-references: field, multiplicative set, localization, integral domain
There are 55 references to this entry.

This is version 3 of fraction field, born on 2001-10-19, modified 2002-03-04.
Object id is 394, canonical name is FractionField.
Accessed 10651 times total.

Classification:
AMS MSC: 13B30 (Commutative rings and algebras :: Ring extensions and related topics :: Quotients and localization)
Pending Errata and Addenda
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Discussion
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isn't this... by drini on 2001-11-08 23:59:11
...also known as quotiens field?

(well.. is it the quotient field I learned in my 1st ring theory course.. am not sure .. never seen it like you show)
 f
G -----> H G
p \ /_ ----- ~ f(G) 
 \ / f ker f 
 G/ker f 
[ reply | up ]
non-commutative version by antizeus on 2001-10-19 23:01:39
Much like localization, there's a lovely theory devoted to non-commutative versions of this, which deserve treatment. Maybe I'll write something later.
[ reply | up ]
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