Integral Domains and Fields : Embedding Theorem
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Problem:
Note: C is set containment
If R is an integral domain, show that the field of quotients Q in the Embedding Theorem is the smallest field containing R in the following sense:
If R C F, where F is a field, show that F has a sub-field K such that R C K and K is isomorphic to Q.
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Proof:
R is an integral domain, it means R is a commutative ring with the multiplicative unit e. Suppose R C F, where F is a field. Now we construct a map f: Q->F. For any element x=a/b in Q, ...
Solution Summary
A proof involving fields is offered in the solution.
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