This research is concerned with two problems in commutative algebra. The principal investigator will analyze the direct-sum decompositions of Cohen-Macaulay modules. She will also study the structure of the partially ordered set of prime ideals in a noetherian ring and the influence of this poset on the direct-sum behavior of modules over the ring. Commutative rings are algebraic structures possessing a commutative addition and a commutative multiplication. These structures occur throughout mathematics and algebra. Common examples include polynomial rings and rings of algebraic integers in extension fields of the rationals. This project is concerned with several questions concerning commutative rings.
