Interesting Linear Algebra Problem

Forum for the GRE subject test in mathematics.
mobius70
Posts: 19
Joined: Thu Jan 24, 2008 1:11 am

Interesting Linear Algebra Problem

Postby mobius70 » Sat Sep 06, 2008 3:31 pm

Hi

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.

Nameless
Posts: 128
Joined: Sun Aug 31, 2008 4:42 pm

Postby Nameless » Sat Sep 06, 2008 3:47 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




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