Let $\mathrm{R}$ be a commutative ring with unity. Which of the following is true?
1. If $\mathrm{R}$ has finitely many prime ideals, then $\mathrm{R}$ 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 $\mathrm{R}$ is an integral domain which has finitely many ideals, then $\mathrm{R}$ is a field