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. Determine whether the following statements are true or false. Justify with a proof or a counterexample. \text { (a) (7 points) If } P \text { and } Q

\text { are both prime ideals of } R \text {, then } P \cap Q \text { is a prime ideal of } R \text {. } (b) (7 points) If F is a field and F is the algebraic closure of F, there is an example where [F : F] isfinite,

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