# Ring theory proof

Modern Algebra

Ring Theory (IX)

The Field of Quotients of an Integral Domain

Prove that the mapping φ:D→F defined by φ(a) = [a , 1] is an isomorphism of D into F ,

where D is the ring of integers and F is the field of quotients of D.

https://brainmass.com/math/ring-theory/ring-theory-proof-fields-98117

#### Solution Preview

see attached

Prove that the mapping defined by is an isomorphism of into ,

where is the ring of integers and is the field of quotients of .

Solution:- The mapping is defined by

,

is a homomorphism.

For any ,

...

#### Solution Summary

This is a ring theory proof regarding an isomorphism.