Forum for the GRE subject test in mathematics.
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- Joined: Thu Jan 24, 2008 1:11 am
Following is the problem.
Prove that each field of characteristic zero contains a copy of the rational number field.
Thanks in advance.
P.S: Source of problem is Hoffman and Kunze.
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- Joined: Sun Aug 31, 2008 4:42 pm
Since Q -rational number field- is the quotient field of Z , this means that Q is the smallest field containing Z. If F is a field whose characteristics is zero AND F contains Z then F has to contain Q since Q is the smallest field containing Z