Forum for the GRE subject test in mathematics.

mobius70
 Posts: 19
 Joined: Thu Jan 24, 2008 1:11 am
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
 Posts: 128
 Joined: Sun Aug 31, 2008 4:42 pm
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