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.
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 ,
This is a ring theory proof regarding an isomorphism.