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  3. let f be a field, and recall the notion of the cha

Let F be a field, and recall the notion of the characteristic of a ring; the...

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Advance Math

Let F be a field, and recall the notion of the characteristic ofa ring; the characteristic of a field is either 0 or a primeinteger.

Show that F has characteristic 0 if and only if it contains acopy of rationals and then F has characteristic p if and only if itcontains a copy of the field Z/pZ.

Show that (in both cases) this determines the smallest subfieldof F.

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