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- Jun 22, 2012

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Exercise 3 in Section 7.5 reads as follows:

Let F be a field. Prove the F contains a unique smallest subfield [TEX] F_0 [/TEX] and that [TEX] F_0 [/TEX] is isomorphic to either [TEX] \mathbb{Q} [/TEX] or [TEX] \mathbb{Z/pZ} [/TEX] for some prime p. (Note: [TEX] F_0 [/TEX] is called prime subfield of F.)

I am somewhat overwhelmed with this exercise and need help to get started. Can anyone help with this exercise.

Peter