Let R be a commutative ring with unity. Which of the following is true?
1. If R has finitely many prime ideals, then R is a field
2. If R has finitely many ideals, then R is finite
3. If R is a P.I.D., then every subring of R with unity is a P.I.D.
4. If R is an integral domain which has finitely many ideals, then R is a field