The field Q(i)={a+ib∣a,b∈Q} and Q(√2)={a+√2b∣a,b∈Q}.Then Show that (a) Q(i) and Q(√2) are isomorphic as Q-vector spaces (b) Show that Q(i) and Q(√2) are not isomorphic as fields
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Originally Posted by makenqau (a) Q(i) and Q(√2) are isomorphic as Q-vector spaces They are isomorphic as vector spaces because they have the same degree over so they are both isomorphic to . (b) Show that Q(i) and Q(√2) are not isomorphic as fields Hint: If is an isomorphism then . Try to get a contradiction from that.
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