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**Coda202** Let D be an integral domain, define phi: Z --> D by phi(n) = n*1, where Z is the set of integers and phi is a homomorphism.

If the char(D) = p, with p not equal to 0, show ker(phi)=pZ and if char(D)=0, show ker(phi)={0}

Using the fundamental theorem of homomorphisms, find a rind which is isomorphic to phi(Z) for both of the above cases.

Finally, let F be a field. If char(F)=p, and p not equal to 0, prove F contains a subfield isomorphic to Z_p.

If char(F)=0, then does F contains a subfield isomorphic to Q