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

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

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

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

Expert Solution

Colby Messinger answered 1 year ago

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