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# fraction field

Related:

Localization, RationalFunction

Synonym:

field of fractions, quotient field

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

13B30*no label found*

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## Comments

## non-commutative version

Much like localization, there's a lovely theory devoted to non-commutative versions of this, which deserve treatment. Maybe I'll write something later.

## isn't this...

...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