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fraction field

Synonym: 
field of fractions, quotient field
Type of Math Object: 
Definition
Major Section: 
Reference
Groups audience: 

Mathematics Subject Classification

13B30 no label found

Comments

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

...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

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