Interesting Linear Algebra Problem

mobius70 · Post by **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 · Post by **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