This research deals with two problems in commutative algebra. The first is to determine if rings with the approximation property are excellent. The second problem is related to the Bass-Quillen conjecture. The study of the geometric properties of rings involves the analysis of the commutative rings that arise in algebraic geometry. This project concerns approximating regular local rings by smooth algebras. While interesting in its own right, it also has application to the Bass-Quillen conjecture on projective modules.
