I need to prove that if K is a field of characteristic (I'll call is "char") 0, then k contains a subfield isomorphic to Q (rationals).(adsbygoogle = window.adsbygoogle || []).push({});

The only way I can think of, is like so (it doesn't seem "good enough").

Let K be a field with char 0. By a certain theorm (in the text), any Integral domain with char 0 contains asubringisomorphic to Z (the integers).

Thus K must also contain a field isomorphic to F_Z (the quotient field of Z)= Q. //

[The last line is a result from another theorem which states that "if K is any field containing an Integral domain isomorphic to D, then K contains a field isomorphic to F_D" - i) Do I need to "show" that the subring isomorphic to Z is an integral domain? ii) Have i lost rigor anywhere?]

thanks

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# Homework Help: Proof re: fields of char 0 and Q

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