Assignment:
Let R1 and R2 be integral domains with quotient fields F1 and F2 respectively. If phi: R1 -> R2 is a ring isomorphism, show that phi extends to an isomorphism phi hat : F1 -> F2. Here extends means that phi hat(a) = phi (a) for all a in R1 (Hint: under the givien assumptions, there is really only one way to define phi hat; of course you still have to prove that phi hat is well-defined and is an isomorphism).
Provide complete and step by step solution for the question and show calculations and use formulas.