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Ring theory proof

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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.

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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.