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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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    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.